1228 lines
69 KiB
Plaintext
1228 lines
69 KiB
Plaintext
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#SIXFORMAT GapDocGAP
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HELPBOOKINFOSIXTMP := rec(
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encoding := "UTF-8",
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bookname := "loops",
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entries :=
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[ [ "Title page", ".", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5" ],
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[ "Copyright", ".-1", [ 0, 0, 1 ], 30, 2, "copyright", "X81488B807F2A1CF1" ]
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, [ "Table of Contents", ".-2", [ 0, 0, 2 ], 35, 3, "table of contents",
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"X8537FEB07AF2BEC8" ],
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[ "\033[1X\033[33X\033[0;-2YIntroduction\033[133X\033[101X", "1",
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[ 1, 0, 0 ], 1, 6, "introduction", "X7DFB63A97E67C0A1" ],
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[ "\033[1X\033[33X\033[0;-2YLicense\033[133X\033[101X", "1.1", [ 1, 1, 0 ],
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13, 6, "license", "X861E5DF986F89AE2" ],
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[ "\033[1X\033[33X\033[0;-2YInstallation\033[133X\033[101X", "1.2",
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[ 1, 2, 0 ], 20, 6, "installation", "X8360C04082558A12" ],
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[ "\033[1X\033[33X\033[0;-2YDocumentation\033[133X\033[101X", "1.3",
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[ 1, 3, 0 ], 43, 6, "documentation", "X7F4F8D6F7CD6B765" ],
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[ "\033[1X\033[33X\033[0;-2YTest Files\033[133X\033[101X", "1.4",
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[ 1, 4, 0 ], 61, 7, "test files", "X801051CC86594630" ],
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[ "\033[1X\033[33X\033[0;-2YMemory Management\033[133X\033[101X", "1.5",
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[ 1, 5, 0 ], 68, 7, "memory management", "X79342B4E7E55FD0F" ],
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[ "\033[1X\033[33X\033[0;-2YFeedback\033[133X\033[101X", "1.6",
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[ 1, 6, 0 ], 76, 7, "feedback", "X80D704CC7EBFDF7A" ],
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[ "\033[1X\033[33X\033[0;-2YAcknowledgment\033[133X\033[101X", "1.7",
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[ 1, 7, 0 ], 83, 7, "acknowledgment", "X811B08C07BD79486" ],
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[ "\033[1X\033[33X\033[0;-2YMathematical Background\033[133X\033[101X",
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"2", [ 2, 0, 0 ], 1, 8, "mathematical background", "X7EF1B6708069B0C7" ]
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, [ "\033[1X\033[33X\033[0;-2YQuasigroups and Loops\033[133X\033[101X",
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"2.1", [ 2, 1, 0 ], 11, 8, "quasigroups and loops", "X80243DE5826583B8"
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], [ "\033[1X\033[33X\033[0;-2YTranslations\033[133X\033[101X", "2.2",
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[ 2, 2, 0 ], 37, 8, "translations", "X7EC01B437CC2B2C9" ],
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[ "\033[1X\033[33X\033[0;-2YSubquasigroups and Subloops\033[133X\033[101X",
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"2.3", [ 2, 3, 0 ], 62, 9, "subquasigroups and subloops",
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"X83EDF04F7952143F" ],
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[ "\033[1X\033[33X\033[0;-2YNilpotence and Solvability\033[133X\033[101X",
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"2.4", [ 2, 4, 0 ], 81, 9, "nilpotence and solvability",
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"X869CBCE381E2C422" ],
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[ "\033[1X\033[33X\033[0;-2YAssociators and Commutators\033[133X\033[101X",
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||
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"2.5", [ 2, 5, 0 ], 95, 9, "associators and commutators",
|
||
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"X7E0849977869E53D" ],
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[ "\033[1X\033[33X\033[0;-2YHomomorphism and Homotopisms\033[133X\033[101X",
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"2.6", [ 2, 6, 0 ], 110, 9, "homomorphism and homotopisms",
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"X791066ED7DD9F254" ],
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[ "\033[1X\033[33X\033[0;-2YHow the Package Works\033[133X\033[101X", "3",
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[ 3, 0, 0 ], 1, 11, "how the package works", "X7A6DF65E826B8CFF" ],
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[ "\033[1X\033[33X\033[0;-2YRepresenting Quasigroups\033[133X\033[101X",
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"3.1", [ 3, 1, 0 ], 18, 11, "representing quasigroups",
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"X86F02BBD87FEA1C6" ],
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[
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"\033[1X\033[33X\033[0;-2YConversions between magmas, quasigroups, loops an\
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d groups\033[133X\033[101X", "3.2", [ 3, 2, 0 ], 48, 12,
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"conversions between magmas quasigroups loops and groups",
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"X807D76EF81B9D061" ],
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[ "\033[1X\033[33X\033[0;-2YCalculating with Quasigroups\033[133X\033[101X",
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"3.3", [ 3, 3, 0 ], 80, 12, "calculating with quasigroups",
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"X87E49ED884FA6DC4" ],
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[
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"\033[1X\033[33X\033[0;-2YNaming, Viewing and Printing Quasigroups and thei\
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r Elements\033[133X\033[101X", "3.4", [ 3, 4, 0 ], 118, 13,
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"naming viewing and printing quasigroups and their elements",
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"X7D75C7A6787AF72A" ],
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[
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"\033[1X\033[33X\033[0;-2YSetQuasigroupElmName and SetLoopElmName\033[133X\\
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033[101X", "3.4-1", [ 3, 4, 1 ], 139, 13,
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"setquasigroupelmname and setloopelmname", "X7A7EB1B579273D07" ],
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[
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"\033[1X\033[33X\033[0;-2YCreating Quasigroups and Loops\033[133X\033[101X"
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, "4", [ 4, 0, 0 ], 1, 14, "creating quasigroups and loops",
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"X7AA4B9C0877550ED" ],
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[ "\033[1X\033[33X\033[0;-2YAbout Cayley Tables\033[133X\033[101X", "4.1",
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[ 4, 1, 0 ], 7, 14, "about cayley tables", "X7DE8405B82BC36A9" ],
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[ "\033[1X\033[33X\033[0;-2YTesting Cayley Tables\033[133X\033[101X",
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"4.2", [ 4, 2, 0 ], 32, 14, "testing cayley tables",
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"X7827BF877AA87246" ],
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[
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"\033[1X\033[33X\033[0;-2YIsQuasigroupTable and IsQuasigroupCayleyTable\\
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033[133X\033[101X", "4.2-1", [ 4, 2, 1 ], 35, 14,
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"isquasigrouptable and isquasigroupcayleytable", "X81179355869B9DFE" ],
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[ "\033[1X\033[33X\033[0;-2YIsLoopTable and IsLoopCayleyTable\033[133X\033[1\
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01X", "4.2-2", [ 4, 2, 2 ], 42, 14, "islooptable and isloopcayleytable",
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"X7AAE48507A471069" ],
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[
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"\033[1X\033[33X\033[0;-2YCanonical and Normalized Cayley Tables\033[133X\\
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033[101X", "4.3", [ 4, 3, 0 ], 52, 15,
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"canonical and normalized cayley tables", "X7BA749CA7DB4EA87" ],
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[
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"\033[1X\033[33X\033[0;-2YCreating Quasigroups and Loops From Cayley Tables\
|
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\033[133X\033[101X", "4.4", [ 4, 4, 0 ], 85, 15,
|
||
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"creating quasigroups and loops from cayley tables",
|
||
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"X7C2372BB8739C5A2" ],
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[
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"\033[1X\033[33X\033[0;-2YQuasigroupByCayleyTable and LoopByCayleyTable\\
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033[133X\033[101X", "4.4-1", [ 4, 4, 1 ], 88, 15,
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"quasigroupbycayleytable and loopbycayleytable", "X860135BB85F2DB19" ],
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[ "\033[1X\033[33X\033[0;-2YCreating Quasigroups and Loops from a File\033[1\
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33X\033[101X", "4.5", [ 4, 5, 0 ], 111, 16,
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"creating quasigroups and loops from a file", "X849944F17E2B37F8" ],
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[
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"\033[1X\033[33X\033[0;-2YQuasigroupFromFile and LoopFromFile\033[133X\033[\
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101X", "4.5-1", [ 4, 5, 1 ], 179, 17, "quasigroupfromfile and loopfromfile",
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"X81A1DB918057933E" ],
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[
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"\033[1X\033[33X\033[0;-2YCreating Quasigroups and Loops From Sections\033[\
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133X\033[101X", "4.6", [ 4, 6, 0 ], 188, 17,
|
||
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"creating quasigroups and loops from sections", "X820E67F88319C38B" ],
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[ "\033[1X\033[33X\033[0;-2YQuasigroupByLeftSection and LoopByLeftSection\
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\033[133X\033[101X", "4.6-2", [ 4, 6, 2 ], 204, 17,
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"quasigroupbyleftsection and loopbyleftsection", "X7EC1EB0D7B8382A1" ],
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[ "\033[1X\033[33X\033[0;-2YQuasigroupByRightSection and LoopByRightSection\
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\033[133X\033[101X", "4.6-3", [ 4, 6, 3 ], 218, 17,
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"quasigroupbyrightsection and loopbyrightsection", "X80B436ED7CC0749E" ]
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,
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[
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"\033[1X\033[33X\033[0;-2YCreating Quasigroups and Loops From Folders\033[1\
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33X\033[101X", "4.7", [ 4, 7, 0 ], 237, 18,
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"creating quasigroups and loops from folders", "X85ABE99E84E5B0E8" ],
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[
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"\033[1X\033[33X\033[0;-2YQuasigroupByRightFolder and LoopByRightFolder\\
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033[133X\033[101X", "4.7-1", [ 4, 7, 1 ], 249, 18,
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"quasigroupbyrightfolder and loopbyrightfolder", "X83168E62861F70AB" ],
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[ "\033[1X\033[33X\033[0;-2YCreating Quasigroups and Loops By Nuclear Extens\
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||
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ions\033[133X\033[101X", "4.8", [ 4, 8, 0 ], 269, 18,
|
||
|
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"creating quasigroups and loops by nuclear extensions",
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||
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"X8759431780AC81A9" ],
|
||
|
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[ "\033[1X\033[33X\033[0;-2YRandom Quasigroups and Loops\033[133X\033[101X",
|
||
|
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"4.9", [ 4, 9, 0 ], 313, 19, "random quasigroups and loops",
|
||
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"X7AE29A1A7AA5C25A" ],
|
||
|
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[
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"\033[1X\033[33X\033[0;-2YRandomQuasigroup and RandomLoop\033[133X\033[101X\
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", "4.9-1", [ 4, 9, 1 ], 338, 19, "randomquasigroup and randomloop",
|
||
|
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"X8271C0F5786B6FA9" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YConversions\033[133X\033[101X", "4.10",
|
||
|
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[ 4, 10, 0 ], 367, 20, "conversions", "X7BC2D8877A943D74" ],
|
||
|
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[
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"\033[1X\033[33X\033[0;-2YProducts of Quasigroups and Loops\033[133X\033[10\
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1X", "4.11", [ 4, 11, 0 ], 425, 21, "products of quasigroups and loops",
|
||
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"X79B7327C79029086" ],
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[
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"\033[1X\033[33X\033[0;-2YOpposite Quasigroups and Loops\033[133X\033[101X"
|
||
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, "4.12", [ 4, 12, 0 ], 437, 21, "opposite quasigroups and loops",
|
||
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"X7865FC8D7854C2E3" ],
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|
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[
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"\033[1X\033[33X\033[0;-2YOpposite, OppositeQuasigroup and OppositeLoop\\
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033[133X\033[101X", "4.12-1", [ 4, 12, 1 ], 444, 21,
|
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|
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"opposite oppositequasigroup and oppositeloop", "X87B6AED47EE2BCD3" ],
|
||
|
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[ "\033[1X\033[33X\033[0;-2YBasic Methods And Attributes\033[133X\033[101X",
|
||
|
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"5", [ 5, 0, 0 ], 1, 22, "basic methods and attributes",
|
||
|
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"X7B9F619279641FAA" ],
|
||
|
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[ "\033[1X\033[33X\033[0;-2YBasic Attributes\033[133X\033[101X", "5.1",
|
||
|
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[ 5, 1, 0 ], 7, 22, "basic attributes", "X8373A7348161DB23" ],
|
||
|
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[ "\033[1X\033[33X\033[0;-2YBasic Arithmetic Operations\033[133X\033[101X",
|
||
|
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"5.2", [ 5, 2, 0 ], 52, 23, "basic arithmetic operations",
|
||
|
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"X82F2CA4A848ABD2B" ],
|
||
|
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[
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||
|
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"\033[1X\033[33X\033[0;-2YLeftDivision and RightDivision\033[133X\033[101X"
|
||
|
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, "5.2-1", [ 5, 2, 1 ], 66, 23, "leftdivision and rightdivision",
|
||
|
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"X7D5956967BCC1834" ],
|
||
|
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[
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"\033[1X\033[33X\033[0;-2YLeftDivisionCayleyTable and RightDivisionCayleyTa\
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ble\033[133X\033[101X", "5.2-2", [ 5, 2, 2 ], 85, 23,
|
||
|
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"leftdivisioncayleytable and rightdivisioncayleytable",
|
||
|
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"X804F67C8796A0EB3" ],
|
||
|
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[ "\033[1X\033[33X\033[0;-2YPowers and Inverses\033[133X\033[101X", "5.3",
|
||
|
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[ 5, 3, 0 ], 93, 23, "powers and inverses", "X810850247ADB4EE9" ],
|
||
|
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[
|
||
|
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"\033[1X\033[33X\033[0;-2YLeftInverse, RightInverse and Inverse\033[133X\\
|
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033[101X", "5.3-1", [ 5, 3, 1 ], 108, 24,
|
||
|
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"leftinverse rightinverse and inverse", "X805781838020CF44" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YAssociators and Commutators\033[133X\033[101X",
|
||
|
|
"5.4", [ 5, 4, 0 ], 130, 24, "associators and commutators",
|
||
|
|
"X7E0849977869E53D" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YGenerators\033[133X\033[101X", "5.5",
|
||
|
|
[ 5, 5, 0 ], 145, 24, "generators", "X7BD5B55C802805B4" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YGeneratorsOfQuasigroup and GeneratorsOfLoop\033[1\
|
||
|
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33X\033[101X", "5.5-1", [ 5, 5, 1 ], 148, 24,
|
||
|
|
"generatorsofquasigroup and generatorsofloop", "X83944A777D161D10" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YMethods Based on Permutation Groups\033[133X\033[\
|
||
|
|
101X", "6", [ 6, 0, 0 ], 1, 26, "methods based on permutation groups",
|
||
|
|
"X794A04C5854D352B" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YParent of a Quasigroup\033[133X\033[101X",
|
||
|
|
"6.1", [ 6, 1, 0 ], 11, 26, "parent of a quasigroup",
|
||
|
|
"X8731D818827C08F3" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YSubquasigroups and Subloops\033[133X\033[101X",
|
||
|
|
"6.2", [ 6, 2, 0 ], 62, 27, "subquasigroups and subloops",
|
||
|
|
"X83EDF04F7952143F" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YIsSubquasigroup and IsSubloop\033[133X\033[101X"
|
||
|
|
, "6.2-3", [ 6, 2, 3 ], 93, 27, "issubquasigroup and issubloop",
|
||
|
|
"X87AC8B7E80CE9260" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YTranslations and Sections\033[133X\033[101X",
|
||
|
|
"6.3", [ 6, 3, 0 ], 133, 28, "translations and sections",
|
||
|
|
"X78AA3D177CCA49FF" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YLeftTranslation and RightTranslation\033[133X\\
|
||
|
|
033[101X", "6.3-1", [ 6, 3, 1 ], 143, 28,
|
||
|
|
"lefttranslation and righttranslation", "X7B45B48C7C4D6061" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YLeftSection and RightSection\033[133X\033[101X",
|
||
|
|
"6.3-2", [ 6, 3, 2 ], 151, 28, "leftsection and rightsection",
|
||
|
|
"X7EB9197C80FB4664" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YMultiplication Groups\033[133X\033[101X",
|
||
|
|
"6.4", [ 6, 4, 0 ], 190, 29, "multiplication groups",
|
||
|
|
"X78ED50F578A88046" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YLeftMutliplicationGroup, RightMultiplicationGroup\
|
||
|
|
and MultiplicationGroup\033[133X\033[101X", "6.4-1", [ 6, 4, 1 ], 193, 29,
|
||
|
|
"leftmutliplicationgroup rightmultiplicationgroup and multiplicationgrou\
|
||
|
|
p", "X87302BE983A5FC61" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YRelativeLeftMultiplicationGroup, RelativeRightMul\
|
||
|
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tiplicationGroup and RelativeMultiplicationGroup\033[133X\033[101X", "6.4-2",
|
||
|
|
[ 6, 4, 2 ], 203, 29,
|
||
|
|
"relativeleftmultiplicationgroup relativerightmultiplicationgroup and re\
|
||
|
|
lativemultiplicationgroup", "X847256B779E1E7E5" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YInner Mapping Groups\033[133X\033[101X", "6.5",
|
||
|
|
[ 6, 5, 0 ], 220, 29, "inner mapping groups", "X8740D61178ACD217" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YLeftInnerMapping, RightInnerMapping, MiddleInnerM\
|
||
|
|
apping\033[133X\033[101X", "6.5-1", [ 6, 5, 1 ], 231, 30,
|
||
|
|
"leftinnermapping rightinnermapping middleinnermapping",
|
||
|
|
"X7EE1E78C856C6F7C" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YLeftInnerMappingGroup, RightInnerMappingGroup, Mi\
|
||
|
|
ddleInnerMappingGroup\033[133X\033[101X", "6.5-2", [ 6, 5, 2 ], 240, 30,
|
||
|
|
"leftinnermappinggroup rightinnermappinggroup middleinnermappinggroup",
|
||
|
|
"X79CDA09A7D48BF2B" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YNuclei, Commutant, Center, and Associator Subloop\
|
||
|
|
\033[133X\033[101X", "6.6", [ 6, 6, 0 ], 268, 30,
|
||
|
|
"nuclei commutant center and associator subloop", "X7B45C2AF7C2E28AB" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YLeftNucles, MiddleNucleus, and RightNucleus\033[\
|
||
|
|
133X\033[101X", "6.6-1", [ 6, 6, 1 ], 273, 30,
|
||
|
|
"leftnucles middlenucleus and rightnucleus", "X7DF536FC85BBD1D2" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YNuc, NucleusOfQuasigroup and NucleusOfLoop\033[13\
|
||
|
|
3X\033[101X", "6.6-2", [ 6, 6, 2 ], 282, 31,
|
||
|
|
"nuc nucleusofquasigroup and nucleusofloop", "X84D389677A91C290" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YNormal Subloops and Simple Loops\033[133X\033[101\
|
||
|
|
X", "6.7", [ 6, 7, 0 ], 320, 31, "normal subloops and simple loops",
|
||
|
|
"X85B650D284FE39F3" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YFactor Loops\033[133X\033[101X", "6.8",
|
||
|
|
[ 6, 8, 0 ], 346, 32, "factor loops", "X87F66DB383C29A4A" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YNilpotency and Central Series\033[133X\033[101X"
|
||
|
|
, "6.9", [ 6, 9, 0 ], 373, 32, "nilpotency and central series",
|
||
|
|
"X821F40748401D698" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YSolvability, Derived Series and Frattini Subloop\\
|
||
|
|
033[133X\033[101X", "6.10", [ 6, 10, 0 ], 411, 33,
|
||
|
|
"solvability derived series and frattini subloop", "X83A38A6C7EDBCA63" ]
|
||
|
|
,
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YFrattiniSubloop and FrattinifactorSize\033[133X\\
|
||
|
|
033[101X", "6.10-4", [ 6, 10, 4 ], 432, 33,
|
||
|
|
"frattinisubloop and frattinifactorsize", "X85BD2C517FA7A47E" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YIsomorphisms and Automorphisms\033[133X\033[101X"
|
||
|
|
, "6.11", [ 6, 11, 0 ], 444, 33, "isomorphisms and automorphisms",
|
||
|
|
"X81F3496578EAA74E" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YIsotopisms\033[133X\033[101X", "6.12",
|
||
|
|
[ 6, 12, 0 ], 532, 35, "isotopisms", "X7E996BDD81E594F9" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YTesting Properties of Quasigroups and Loops\033[1\
|
||
|
|
33X\033[101X", "7", [ 7, 0, 0 ], 1, 36,
|
||
|
|
"testing properties of quasigroups and loops", "X7910E575825C713E" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YAssociativity, Commutativity and Generalizations\\
|
||
|
|
033[133X\033[101X", "7.1", [ 7, 1, 0 ], 16, 36,
|
||
|
|
"associativity commutativity and generalizations", "X7960E3FB7A7F0F00" ]
|
||
|
|
, [ "\033[1X\033[33X\033[0;-2YInverse Propeties\033[133X\033[101X",
|
||
|
|
"7.2", [ 7, 2, 0 ], 46, 37, "inverse propeties", "X853841C5820BFEA4" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YHasLeftInverseProperty, HasRightInverseProperty \
|
||
|
|
and HasInverseProperty\033[133X\033[101X", "7.2-1", [ 7, 2, 1 ], 53, 37,
|
||
|
|
"hasleftinverseproperty hasrightinverseproperty and hasinverseproperty",
|
||
|
|
"X85EDD10586596458" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YSome Properties of Quasigroups\033[133X\033[101X"
|
||
|
|
, "7.3", [ 7, 3, 0 ], 102, 38, "some properties of quasigroups",
|
||
|
|
"X7D8CB6DA828FD744" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YIsLeftDistributive, IsRightDistributive, IsDistri\
|
||
|
|
butive\033[133X\033[101X", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"isleftdistributive isrightdistributive isdistributive",
|
||
|
|
"X7B76FD6E878ED4F1" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YIsEntropic and IsMedial\033[133X\033[101X",
|
||
|
|
"7.3-7", [ 7, 3, 7 ], 160, 39, "isentropic and ismedial",
|
||
|
|
"X7F23D4D97A38D223" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YLoops of Bol Moufang Type\033[133X\033[101X",
|
||
|
|
"7.4", [ 7, 4, 0 ], 170, 39, "loops of bol moufang type",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YPower Alternative Loops\033[133X\033[101X",
|
||
|
|
"7.5", [ 7, 5, 0 ], 324, 42, "power alternative loops",
|
||
|
|
"X83A501387E1AC371" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YIsLeftPowerAlternative, IsRightPowerAlternative a\
|
||
|
|
nd IsPowerAlternative\033[133X\033[101X", "7.5-1", [ 7, 5, 1 ], 337, 42,
|
||
|
|
"isleftpoweralternative isrightpoweralternative and ispoweralternative",
|
||
|
|
"X875C3DF681B3FAE2" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YConjugacy Closed Loops and Related Properties\\
|
||
|
|
033[133X\033[101X", "7.6", [ 7, 6, 0 ], 346, 42,
|
||
|
|
"conjugacy closed loops and related properties", "X8176B2C47A4629CD" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YAutomorphic Loops\033[133X\033[101X", "7.7",
|
||
|
|
[ 7, 7, 0 ], 384, 43, "automorphic loops", "X793B22EA8643C667" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YAdditonal Varieties of Loops\033[133X\033[101X",
|
||
|
|
"7.8", [ 7, 8, 0 ], 451, 44, "additonal varieties of loops",
|
||
|
|
"X846F363879BAB349" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YIsLeftBruckLoop and IsLeftKLoop\033[133X\033[101X\
|
||
|
|
", "7.8-3", [ 7, 8, 3 ], 470, 44, "isleftbruckloop and isleftkloop",
|
||
|
|
"X85F1BD4280E44F5B" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YIsRightBruckLoop and IsRightKLoop\033[133X\033[10\
|
||
|
|
1X", "7.8-4", [ 7, 8, 4 ], 480, 44, "isrightbruckloop and isrightkloop",
|
||
|
|
"X857B373E7B4E0519" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YSpecific Methods\033[133X\033[101X", "8",
|
||
|
|
[ 8, 0, 0 ], 1, 45, "specific methods", "X85AFC9C47FD3C03F" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YCore Methods for Bol Loops\033[133X\033[101X",
|
||
|
|
"8.1", [ 8, 1, 0 ], 7, 45, "core methods for bol loops",
|
||
|
|
"X7990F2F880E717EE" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YAssociatedLeftBruckLoop and AssociatedRightBruckL\
|
||
|
|
oop\033[133X\033[101X", "8.1-1", [ 8, 1, 1 ], 10, 45,
|
||
|
|
"associatedleftbruckloop and associatedrightbruckloop",
|
||
|
|
"X8664CA927DD73DBE" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YMoufang Modifications\033[133X\033[101X",
|
||
|
|
"8.2", [ 8, 2, 0 ], 47, 46, "moufang modifications",
|
||
|
|
"X819F82737C2A860D" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YTriality for Moufang Loops\033[133X\033[101X",
|
||
|
|
"8.3", [ 8, 3, 0 ], 98, 46, "triality for moufang loops",
|
||
|
|
"X83E73A767D79FAFD" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YRealizing Groups as Multiplication Groups of Loop\
|
||
|
|
s\033[133X\033[101X", "8.4", [ 8, 4, 0 ], 127, 47,
|
||
|
|
"realizing groups as multiplication groups of loops",
|
||
|
|
"X841ED66B8084AA73" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YLibraries of Loops\033[133X\033[101X", "9",
|
||
|
|
[ 9, 0, 0 ], 1, 49, "libraries of loops", "X7BF3EE6E7953560D" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YA Typical Library\033[133X\033[101X", "9.1",
|
||
|
|
[ 9, 1, 0 ], 7, 49, "a typical library", "X874DFEAA79B3377C" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YLeft Bol Loops and Right Bol Loops\033[133X\033[1\
|
||
|
|
01X", "9.2", [ 9, 2, 0 ], 54, 50, "left bol loops and right bol loops",
|
||
|
|
"X7DF21BD685FBF258" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YMoufang Loops\033[133X\033[101X", "9.3",
|
||
|
|
[ 9, 3, 0 ], 80, 50, "moufang loops", "X7953702D84E60AF4" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YCode Loops\033[133X\033[101X", "9.4",
|
||
|
|
[ 9, 4, 0 ], 109, 51, "code loops", "X7BCA6BCB847F79DC" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YSteiner Loops\033[133X\033[101X", "9.5",
|
||
|
|
[ 9, 5, 0 ], 122, 51, "steiner loops", "X84E941EE7846D3EE" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YConjugacy Closed Loops\033[133X\033[101X",
|
||
|
|
"9.6", [ 9, 6, 0 ], 149, 51, "conjugacy closed loops",
|
||
|
|
"X867E5F0783FEB8B5" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YRCCLoop and RightConjugacyClosedLoop\033[133X\\
|
||
|
|
033[101X", "9.6-1", [ 9, 6, 1 ], 173, 52,
|
||
|
|
"rccloop and rightconjugacyclosedloop", "X806B2DE67990E42F" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YLCCLoop and LeftConjugacyClosedLoop\033[133X\033[\
|
||
|
|
101X", "9.6-2", [ 9, 6, 2 ], 180, 52, "lccloop and leftconjugacyclosedloop",
|
||
|
|
"X80AB8B107D55FB19" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YCCLoop and ConjugacyClosedLoop\033[133X\033[101X"
|
||
|
|
, "9.6-3", [ 9, 6, 3 ], 217, 52, "ccloop and conjugacyclosedloop",
|
||
|
|
"X798BC601843E8916" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YSmall Loops\033[133X\033[101X", "9.7",
|
||
|
|
[ 9, 7, 0 ], 224, 52, "small loops", "X7E3A8F2C790F2CA1" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YPaige Loops\033[133X\033[101X", "9.8",
|
||
|
|
[ 9, 8, 0 ], 235, 53, "paige loops", "X8135C8FD8714C606" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YNilpotent Loops\033[133X\033[101X", "9.9",
|
||
|
|
[ 9, 9, 0 ], 250, 53, "nilpotent loops", "X86695C577A4D1784" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YAutomorphic Loops\033[133X\033[101X", "9.10",
|
||
|
|
[ 9, 10, 0 ], 266, 53, "automorphic loops", "X793B22EA8643C667" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YInteresting Loops\033[133X\033[101X", "9.11",
|
||
|
|
[ 9, 11, 0 ], 283, 54, "interesting loops", "X843BD73F788049F7" ],
|
||
|
|
[
|
||
|
|
"\033[1X\033[33X\033[0;-2YLibraries of Loops Up To Isotopism\033[133X\033[1\
|
||
|
|
01X", "9.12", [ 9, 12, 0 ], 298, 54, "libraries of loops up to isotopism",
|
||
|
|
"X864839227D5C0A90" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YFiles\033[133X\033[101X", "a", [ "A", 0, 0 ],
|
||
|
|
1, 55, "files", "X7BC4571A79FFB7D0" ],
|
||
|
|
[ "\033[1X\033[33X\033[0;-2YFilters\033[133X\033[101X", "b", [ "B", 0, 0 ],
|
||
|
|
1, 57, "filters", "X84EFA4C07D4277BB" ],
|
||
|
|
[ "Bibliography", "bib", [ "Bib", 0, 0 ], 1, 60, "bibliography",
|
||
|
|
"X7A6F98FD85F02BFE" ],
|
||
|
|
[ "References", "bib", [ "Bib", 0, 0 ], 1, 60, "references",
|
||
|
|
"X7A6F98FD85F02BFE" ],
|
||
|
|
[ "Index", "ind", [ "Ind", 0, 0 ], 1, 62, "index", "X83A0356F839C696F" ],
|
||
|
|
[ "groupoid", "2.1", [ 2, 1, 0 ], 11, 8, "groupoid", "X80243DE5826583B8" ],
|
||
|
|
[ "magma", "2.1", [ 2, 1, 0 ], 11, 8, "magma", "X80243DE5826583B8" ],
|
||
|
|
[ "neutral element", "2.1", [ 2, 1, 0 ], 11, 8, "neutral element",
|
||
|
|
"X80243DE5826583B8" ],
|
||
|
|
[ "identity element", "2.1", [ 2, 1, 0 ], 11, 8, "identity element",
|
||
|
|
"X80243DE5826583B8" ],
|
||
|
|
[ "inverse two-sided", "2.1", [ 2, 1, 0 ], 11, 8, "inverse two-sided",
|
||
|
|
"X80243DE5826583B8" ],
|
||
|
|
[ "group", "2.1", [ 2, 1, 0 ], 11, 8, "group", "X80243DE5826583B8" ],
|
||
|
|
[ "quasigroup", "2.1", [ 2, 1, 0 ], 11, 8, "quasigroup",
|
||
|
|
"X80243DE5826583B8" ],
|
||
|
|
[ "latin square", "2.1", [ 2, 1, 0 ], 11, 8, "latin square",
|
||
|
|
"X80243DE5826583B8" ],
|
||
|
|
[ "loop", "2.1", [ 2, 1, 0 ], 11, 8, "loop", "X80243DE5826583B8" ],
|
||
|
|
[ "translation left", "2.2", [ 2, 2, 0 ], 37, 8, "translation left",
|
||
|
|
"X7EC01B437CC2B2C9" ],
|
||
|
|
[ "translation right", "2.2", [ 2, 2, 0 ], 37, 8, "translation right",
|
||
|
|
"X7EC01B437CC2B2C9" ],
|
||
|
|
[ "division left", "2.2", [ 2, 2, 0 ], 37, 8, "division left",
|
||
|
|
"X7EC01B437CC2B2C9" ],
|
||
|
|
[ "division right", "2.2", [ 2, 2, 0 ], 37, 8, "division right",
|
||
|
|
"X7EC01B437CC2B2C9" ],
|
||
|
|
[ "section left", "2.2", [ 2, 2, 0 ], 37, 8, "section left",
|
||
|
|
"X7EC01B437CC2B2C9" ],
|
||
|
|
[ "section right", "2.2", [ 2, 2, 0 ], 37, 8, "section right",
|
||
|
|
"X7EC01B437CC2B2C9" ],
|
||
|
|
[ "multiplication group left", "2.2", [ 2, 2, 0 ], 37, 8,
|
||
|
|
"multiplication group left", "X7EC01B437CC2B2C9" ],
|
||
|
|
[ "multiplication group right", "2.2", [ 2, 2, 0 ], 37, 8,
|
||
|
|
"multiplication group right", "X7EC01B437CC2B2C9" ],
|
||
|
|
[ "multiplication group", "2.2", [ 2, 2, 0 ], 37, 8, "multiplication group",
|
||
|
|
"X7EC01B437CC2B2C9" ],
|
||
|
|
[ "inner mapping group left", "2.2", [ 2, 2, 0 ], 37, 8,
|
||
|
|
"inner mapping group left", "X7EC01B437CC2B2C9" ],
|
||
|
|
[ "inner mapping group right", "2.2", [ 2, 2, 0 ], 37, 8,
|
||
|
|
"inner mapping group right", "X7EC01B437CC2B2C9" ],
|
||
|
|
[ "inner mapping group", "2.2", [ 2, 2, 0 ], 37, 8, "inner mapping group",
|
||
|
|
"X7EC01B437CC2B2C9" ],
|
||
|
|
[ "subquasigroup", "2.3", [ 2, 3, 0 ], 62, 9, "subquasigroup",
|
||
|
|
"X83EDF04F7952143F" ],
|
||
|
|
[ "subloop", "2.3", [ 2, 3, 0 ], 62, 9, "subloop", "X83EDF04F7952143F" ],
|
||
|
|
[ "nucleus left", "2.3", [ 2, 3, 0 ], 62, 9, "nucleus left",
|
||
|
|
"X83EDF04F7952143F" ],
|
||
|
|
[ "nucleus middle", "2.3", [ 2, 3, 0 ], 62, 9, "nucleus middle",
|
||
|
|
"X83EDF04F7952143F" ],
|
||
|
|
[ "nucleus right", "2.3", [ 2, 3, 0 ], 62, 9, "nucleus right",
|
||
|
|
"X83EDF04F7952143F" ],
|
||
|
|
[ "nucleus", "2.3", [ 2, 3, 0 ], 62, 9, "nucleus", "X83EDF04F7952143F" ],
|
||
|
|
[ "commutant", "2.3", [ 2, 3, 0 ], 62, 9, "commutant", "X83EDF04F7952143F" ]
|
||
|
|
, [ "center", "2.3", [ 2, 3, 0 ], 62, 9, "center", "X83EDF04F7952143F" ],
|
||
|
|
[ "subloop normal", "2.3", [ 2, 3, 0 ], 62, 9, "subloop normal",
|
||
|
|
"X83EDF04F7952143F" ],
|
||
|
|
[ "nilpotence class", "2.4", [ 2, 4, 0 ], 81, 9, "nilpotence class",
|
||
|
|
"X869CBCE381E2C422" ],
|
||
|
|
[ "nilpotent loop", "2.4", [ 2, 4, 0 ], 81, 9, "nilpotent loop",
|
||
|
|
"X869CBCE381E2C422" ],
|
||
|
|
[ "loop nilpotent", "2.4", [ 2, 4, 0 ], 81, 9, "loop nilpotent",
|
||
|
|
"X869CBCE381E2C422" ],
|
||
|
|
[ "central series upper", "2.4", [ 2, 4, 0 ], 81, 9, "central series upper",
|
||
|
|
"X869CBCE381E2C422" ],
|
||
|
|
[ "derived subloop", "2.4", [ 2, 4, 0 ], 81, 9, "derived subloop",
|
||
|
|
"X869CBCE381E2C422" ],
|
||
|
|
[ "solvability class", "2.4", [ 2, 4, 0 ], 81, 9, "solvability class",
|
||
|
|
"X869CBCE381E2C422" ],
|
||
|
|
[ "solvable loop", "2.4", [ 2, 4, 0 ], 81, 9, "solvable loop",
|
||
|
|
"X869CBCE381E2C422" ],
|
||
|
|
[ "loop solvable", "2.4", [ 2, 4, 0 ], 81, 9, "loop solvable",
|
||
|
|
"X869CBCE381E2C422" ],
|
||
|
|
[ "derived series", "2.4", [ 2, 4, 0 ], 81, 9, "derived series",
|
||
|
|
"X869CBCE381E2C422" ],
|
||
|
|
[ "commutator", "2.5", [ 2, 5, 0 ], 95, 9, "commutator",
|
||
|
|
"X7E0849977869E53D" ],
|
||
|
|
[ "associator", "2.5", [ 2, 5, 0 ], 95, 9, "associator",
|
||
|
|
"X7E0849977869E53D" ],
|
||
|
|
[ "associator subloop", "2.5", [ 2, 5, 0 ], 95, 9, "associator subloop",
|
||
|
|
"X7E0849977869E53D" ],
|
||
|
|
[ "homomorphism", "2.6", [ 2, 6, 0 ], 110, 9, "homomorphism",
|
||
|
|
"X791066ED7DD9F254" ],
|
||
|
|
[ "isomorphism", "2.6", [ 2, 6, 0 ], 110, 9, "isomorphism",
|
||
|
|
"X791066ED7DD9F254" ],
|
||
|
|
[ "homotopism", "2.6", [ 2, 6, 0 ], 110, 9, "homotopism",
|
||
|
|
"X791066ED7DD9F254" ],
|
||
|
|
[ "isotopism", "2.6", [ 2, 6, 0 ], 110, 9, "isotopism", "X791066ED7DD9F254"
|
||
|
|
],
|
||
|
|
[ "isotopism principal", "2.6", [ 2, 6, 0 ], 110, 9, "isotopism principal",
|
||
|
|
"X791066ED7DD9F254" ],
|
||
|
|
[ "loop isotope principal", "2.6", [ 2, 6, 0 ], 110, 9,
|
||
|
|
"loop isotope principal", "X791066ED7DD9F254" ],
|
||
|
|
[ "IsQuasigroupElement", "3.1", [ 3, 1, 0 ], 18, 11, "isquasigroupelement",
|
||
|
|
"X86F02BBD87FEA1C6" ],
|
||
|
|
[ "IsLoopElement", "3.1", [ 3, 1, 0 ], 18, 11, "isloopelement",
|
||
|
|
"X86F02BBD87FEA1C6" ],
|
||
|
|
[ "IsQuasigroup", "3.1", [ 3, 1, 0 ], 18, 11, "isquasigroup",
|
||
|
|
"X86F02BBD87FEA1C6" ],
|
||
|
|
[ "IsLoop", "3.1", [ 3, 1, 0 ], 18, 11, "isloop", "X86F02BBD87FEA1C6" ],
|
||
|
|
[ "Bol loop left", "3.3", [ 3, 3, 0 ], 80, 12, "bol loop left",
|
||
|
|
"X87E49ED884FA6DC4" ],
|
||
|
|
[ "loop left Bol", "3.3", [ 3, 3, 0 ], 80, 12, "loop left bol",
|
||
|
|
"X87E49ED884FA6DC4" ],
|
||
|
|
[ "simple loop", "3.3", [ 3, 3, 0 ], 80, 12, "simple loop",
|
||
|
|
"X87E49ED884FA6DC4" ],
|
||
|
|
[ "loop simple", "3.3", [ 3, 3, 0 ], 80, 12, "loop simple",
|
||
|
|
"X87E49ED884FA6DC4" ],
|
||
|
|
[ "\033[2XSetQuasigroupElmName\033[102X", "3.4-1", [ 3, 4, 1 ], 139, 13,
|
||
|
|
"setquasigroupelmname", "X7A7EB1B579273D07" ],
|
||
|
|
[ "\033[2XSetLoopElmName\033[102X", "3.4-1", [ 3, 4, 1 ], 139, 13,
|
||
|
|
"setloopelmname", "X7A7EB1B579273D07" ],
|
||
|
|
[ "Cayley table", "4.1", [ 4, 1, 0 ], 7, 14, "cayley table",
|
||
|
|
"X7DE8405B82BC36A9" ],
|
||
|
|
[ "multiplication table", "4.1", [ 4, 1, 0 ], 7, 14, "multiplication table",
|
||
|
|
"X7DE8405B82BC36A9" ],
|
||
|
|
[ "quasigroup table", "4.1", [ 4, 1, 0 ], 7, 14, "quasigroup table",
|
||
|
|
"X7DE8405B82BC36A9" ],
|
||
|
|
[ "latin square", "4.1", [ 4, 1, 0 ], 7, 14, "latin square",
|
||
|
|
"X7DE8405B82BC36A9" ],
|
||
|
|
[ "loop table", "4.1", [ 4, 1, 0 ], 7, 14, "loop table",
|
||
|
|
"X7DE8405B82BC36A9" ],
|
||
|
|
[ "\033[2XIsQuasigroupTable\033[102X", "4.2-1", [ 4, 2, 1 ], 35, 14,
|
||
|
|
"isquasigrouptable", "X81179355869B9DFE" ],
|
||
|
|
[ "\033[2XIsQuasigroupCayleyTable\033[102X", "4.2-1", [ 4, 2, 1 ], 35, 14,
|
||
|
|
"isquasigroupcayleytable", "X81179355869B9DFE" ],
|
||
|
|
[ "\033[2XIsLoopTable\033[102X", "4.2-2", [ 4, 2, 2 ], 42, 14,
|
||
|
|
"islooptable", "X7AAE48507A471069" ],
|
||
|
|
[ "\033[2XIsLoopCayleyTable\033[102X", "4.2-2", [ 4, 2, 2 ], 42, 14,
|
||
|
|
"isloopcayleytable", "X7AAE48507A471069" ],
|
||
|
|
[ "\033[2XCanonicalCayleyTable\033[102X", "4.3-1", [ 4, 3, 1 ], 55, 15,
|
||
|
|
"canonicalcayleytable", "X7971CCB87DAFF7B9" ],
|
||
|
|
[ "Cayley table canonical", "4.3-1", [ 4, 3, 1 ], 55, 15,
|
||
|
|
"cayley table canonical", "X7971CCB87DAFF7B9" ],
|
||
|
|
[ "\033[2XCanonicalCopy\033[102X", "4.3-2", [ 4, 3, 2 ], 65, 15,
|
||
|
|
"canonicalcopy", "X7B816D887F46E6B7" ],
|
||
|
|
[ "\033[2XNormalizedQuasigroupTable\033[102X", "4.3-3", [ 4, 3, 3 ], 74,
|
||
|
|
15, "normalizedquasigrouptable", "X821A2F9E85FAD8BF" ],
|
||
|
|
[ "\033[2XQuasigroupByCayleyTable\033[102X", "4.4-1", [ 4, 4, 1 ], 88, 15,
|
||
|
|
"quasigroupbycayleytable", "X860135BB85F2DB19" ],
|
||
|
|
[ "\033[2XLoopByCayleyTable\033[102X", "4.4-1", [ 4, 4, 1 ], 88, 15,
|
||
|
|
"loopbycayleytable", "X860135BB85F2DB19" ],
|
||
|
|
[ "\033[2XQuasigroupFromFile\033[102X", "4.5-1", [ 4, 5, 1 ], 179, 17,
|
||
|
|
"quasigroupfromfile", "X81A1DB918057933E" ],
|
||
|
|
[ "\033[2XLoopFromFile\033[102X", "4.5-1", [ 4, 5, 1 ], 179, 17,
|
||
|
|
"loopfromfile", "X81A1DB918057933E" ],
|
||
|
|
[ "\033[2XCayleyTableByPerms\033[102X", "4.6-1", [ 4, 6, 1 ], 191, 17,
|
||
|
|
"cayleytablebyperms", "X7F94C8DD7E1A3470" ],
|
||
|
|
[ "\033[2XQuasigroupByLeftSection\033[102X", "4.6-2", [ 4, 6, 2 ], 204, 17,
|
||
|
|
"quasigroupbyleftsection", "X7EC1EB0D7B8382A1" ],
|
||
|
|
[ "\033[2XLoopByLeftSection\033[102X", "4.6-2", [ 4, 6, 2 ], 204, 17,
|
||
|
|
"loopbyleftsection", "X7EC1EB0D7B8382A1" ],
|
||
|
|
[ "\033[2XQuasigroupByRightSection\033[102X", "4.6-3", [ 4, 6, 3 ], 218,
|
||
|
|
17, "quasigroupbyrightsection", "X80B436ED7CC0749E" ],
|
||
|
|
[ "\033[2XLoopByRightSection\033[102X", "4.6-3", [ 4, 6, 3 ], 218, 17,
|
||
|
|
"loopbyrightsection", "X80B436ED7CC0749E" ],
|
||
|
|
[ "folder quasigroup", "4.7", [ 4, 7, 0 ], 237, 18, "folder quasigroup",
|
||
|
|
"X85ABE99E84E5B0E8" ],
|
||
|
|
[ "\033[2XQuasigroupByRightFolder\033[102X", "4.7-1", [ 4, 7, 1 ], 249, 18,
|
||
|
|
"quasigroupbyrightfolder", "X83168E62861F70AB" ],
|
||
|
|
[ "\033[2XLoopByRightFolder\033[102X", "4.7-1", [ 4, 7, 1 ], 249, 18,
|
||
|
|
"loopbyrightfolder", "X83168E62861F70AB" ],
|
||
|
|
[ "extension", "4.8", [ 4, 8, 0 ], 269, 18, "extension",
|
||
|
|
"X8759431780AC81A9" ],
|
||
|
|
[ "extension nuclear", "4.8", [ 4, 8, 0 ], 269, 18, "extension nuclear",
|
||
|
|
"X8759431780AC81A9" ],
|
||
|
|
[ "cocycle", "4.8", [ 4, 8, 0 ], 269, 18, "cocycle", "X8759431780AC81A9" ],
|
||
|
|
[ "\033[2XNuclearExtension\033[102X", "4.8-1", [ 4, 8, 1 ], 283, 18,
|
||
|
|
"nuclearextension", "X784733C67AA6B2FA" ],
|
||
|
|
[ "\033[2XLoopByExtension\033[102X", "4.8-2", [ 4, 8, 2 ], 294, 18,
|
||
|
|
"loopbyextension", "X79AEE93E7E15B802" ],
|
||
|
|
[ "latin square random", "4.9", [ 4, 9, 0 ], 313, 19, "latin square random",
|
||
|
|
"X7AE29A1A7AA5C25A" ],
|
||
|
|
[ "\033[2XRandomQuasigroup\033[102X", "4.9-1", [ 4, 9, 1 ], 338, 19,
|
||
|
|
"randomquasigroup", "X8271C0F5786B6FA9" ],
|
||
|
|
[ "\033[2XRandomLoop\033[102X", "4.9-1", [ 4, 9, 1 ], 338, 19,
|
||
|
|
"randomloop", "X8271C0F5786B6FA9" ],
|
||
|
|
[ "\033[2XRandomNilpotentLoop\033[102X", "4.9-2", [ 4, 9, 2 ], 350, 19,
|
||
|
|
"randomnilpotentloop", "X817132C887D3FD3A" ],
|
||
|
|
[ "loop nilpotent", "4.9-2", [ 4, 9, 2 ], 350, 19, "loop nilpotent",
|
||
|
|
"X817132C887D3FD3A" ],
|
||
|
|
[ "\033[2XIntoQuasigroup\033[102X", "4.10-1", [ 4, 10, 1 ], 382, 20,
|
||
|
|
"intoquasigroup", "X84575A4B78CC545E" ],
|
||
|
|
[ "\033[2XPrincipalLoopIsotope\033[102X", "4.10-2", [ 4, 10, 2 ], 389, 20,
|
||
|
|
"principalloopisotope", "X79CEA57C850C7070" ],
|
||
|
|
[ "\033[2XIntoLoop\033[102X", "4.10-3", [ 4, 10, 3 ], 401, 20, "intoloop",
|
||
|
|
"X7A59C36683118E5A" ],
|
||
|
|
[ "\033[2XIntoGroup\033[102X", "4.10-4", [ 4, 10, 4 ], 416, 20,
|
||
|
|
"intogroup", "X7B5C6C64831B866E" ],
|
||
|
|
[ "\033[2XDirectProduct\033[102X", "4.11-1", [ 4, 11, 1 ], 428, 21,
|
||
|
|
"directproduct", "X861BA02C7902A4F4" ],
|
||
|
|
[ "opposite quasigroup", "4.12", [ 4, 12, 0 ], 437, 21,
|
||
|
|
"opposite quasigroup", "X7865FC8D7854C2E3" ],
|
||
|
|
[ "quasigroup opposite", "4.12", [ 4, 12, 0 ], 437, 21,
|
||
|
|
"quasigroup opposite", "X7865FC8D7854C2E3" ],
|
||
|
|
[ "\033[2XOpposite\033[102X", "4.12-1", [ 4, 12, 1 ], 444, 21, "opposite",
|
||
|
|
"X87B6AED47EE2BCD3" ],
|
||
|
|
[ "\033[2XOppositeQuasigroup\033[102X", "4.12-1", [ 4, 12, 1 ], 444, 21,
|
||
|
|
"oppositequasigroup", "X87B6AED47EE2BCD3" ],
|
||
|
|
[ "\033[2XOppositeLoop\033[102X", "4.12-1", [ 4, 12, 1 ], 444, 21,
|
||
|
|
"oppositeloop", "X87B6AED47EE2BCD3" ],
|
||
|
|
[ "\033[2XElements\033[102X", "5.1-1", [ 5, 1, 1 ], 14, 22, "elements",
|
||
|
|
"X79B130FC7906FB4C" ],
|
||
|
|
[ "\033[2XCayleyTable\033[102X", "5.1-2", [ 5, 1, 2 ], 21, 22,
|
||
|
|
"cayleytable", "X85457FA27DE7114D" ],
|
||
|
|
[ "\033[2XOne\033[102X", "5.1-3", [ 5, 1, 3 ], 28, 22, "one",
|
||
|
|
"X8129A6877FFD804B" ],
|
||
|
|
[ "\033[2XSize\033[102X", "5.1-4", [ 5, 1, 4 ], 37, 22, "size",
|
||
|
|
"X858ADA3B7A684421" ],
|
||
|
|
[ "\033[2XExponent\033[102X", "5.1-5", [ 5, 1, 5 ], 42, 23, "exponent",
|
||
|
|
"X7D44470C7DA59C1C" ],
|
||
|
|
[ "loop power associative", "5.1-5", [ 5, 1, 5 ], 42, 23,
|
||
|
|
"loop power associative", "X7D44470C7DA59C1C" ],
|
||
|
|
[ "power associative loop", "5.1-5", [ 5, 1, 5 ], 42, 23,
|
||
|
|
"power associative loop", "X7D44470C7DA59C1C" ],
|
||
|
|
[ "exponent", "5.1-5", [ 5, 1, 5 ], 42, 23, "exponent", "X7D44470C7DA59C1C"
|
||
|
|
], [ "\033[2XLeftDivision\033[102X", "5.2-1", [ 5, 2, 1 ], 66, 23,
|
||
|
|
"leftdivision", "X7D5956967BCC1834" ],
|
||
|
|
[ "\033[2XRightDivision\033[102X", "5.2-1", [ 5, 2, 1 ], 66, 23,
|
||
|
|
"rightdivision", "X7D5956967BCC1834" ],
|
||
|
|
[ "\033[2XLeftDivision\033[102X", "5.2-1", [ 5, 2, 1 ], 66, 23,
|
||
|
|
"leftdivision", "X7D5956967BCC1834" ],
|
||
|
|
[ "\033[2XLeftDivision\033[102X", "5.2-1", [ 5, 2, 1 ], 66, 23,
|
||
|
|
"leftdivision", "X7D5956967BCC1834" ],
|
||
|
|
[ "\033[2XRightDivision\033[102X", "5.2-1", [ 5, 2, 1 ], 66, 23,
|
||
|
|
"rightdivision", "X7D5956967BCC1834" ],
|
||
|
|
[ "\033[2XRightDivision\033[102X", "5.2-1", [ 5, 2, 1 ], 66, 23,
|
||
|
|
"rightdivision", "X7D5956967BCC1834" ],
|
||
|
|
[ "\033[2XLeftDivisionCayleyTable\033[102X", "5.2-2", [ 5, 2, 2 ], 85, 23,
|
||
|
|
"leftdivisioncayleytable", "X804F67C8796A0EB3" ],
|
||
|
|
[ "\033[2XRightDivisionCayleyTable\033[102X", "5.2-2", [ 5, 2, 2 ], 85, 23,
|
||
|
|
"rightdivisioncayleytable", "X804F67C8796A0EB3" ],
|
||
|
|
[ "inverse left", "5.3", [ 5, 3, 0 ], 93, 23, "inverse left",
|
||
|
|
"X810850247ADB4EE9" ],
|
||
|
|
[ "inverse right", "5.3", [ 5, 3, 0 ], 93, 23, "inverse right",
|
||
|
|
"X810850247ADB4EE9" ],
|
||
|
|
[ "inverse", "5.3", [ 5, 3, 0 ], 93, 23, "inverse", "X810850247ADB4EE9" ],
|
||
|
|
[ "\033[2XLeftInverse\033[102X", "5.3-1", [ 5, 3, 1 ], 108, 24,
|
||
|
|
"leftinverse", "X805781838020CF44" ],
|
||
|
|
[ "\033[2XRightInverse\033[102X", "5.3-1", [ 5, 3, 1 ], 108, 24,
|
||
|
|
"rightinverse", "X805781838020CF44" ],
|
||
|
|
[ "\033[2XInverse\033[102X", "5.3-1", [ 5, 3, 1 ], 108, 24, "inverse",
|
||
|
|
"X805781838020CF44" ],
|
||
|
|
[ "\033[2XAssociator\033[102X", "5.4-1", [ 5, 4, 1 ], 135, 24,
|
||
|
|
"associator", "X82B7448879B91F7B" ],
|
||
|
|
[ "\033[2XCommutator\033[102X", "5.4-2", [ 5, 4, 2 ], 140, 24,
|
||
|
|
"commutator", "X7D624A9587FB1FE5" ],
|
||
|
|
[ "\033[2XGeneratorsOfQuasigroup\033[102X", "5.5-1", [ 5, 5, 1 ], 148, 24,
|
||
|
|
"generatorsofquasigroup", "X83944A777D161D10" ],
|
||
|
|
[ "\033[2XGeneratorsOfLoop\033[102X", "5.5-1", [ 5, 5, 1 ], 148, 24,
|
||
|
|
"generatorsofloop", "X83944A777D161D10" ],
|
||
|
|
[ "\033[2XGeneratorsSmallest\033[102X", "5.5-2", [ 5, 5, 2 ], 160, 25,
|
||
|
|
"generatorssmallest", "X82FD78AF7F80A0E2" ],
|
||
|
|
[ "\033[2XSmallGeneratingSet\033[102X", "5.5-3", [ 5, 5, 3 ], 166, 25,
|
||
|
|
"smallgeneratingset", "X814DBABC878D5232" ],
|
||
|
|
[ "\033[2XParent\033[102X", "6.1-1", [ 6, 1, 1 ], 19, 26, "parent",
|
||
|
|
"X7BC856CC7F116BB0" ],
|
||
|
|
[ "\033[2XPosition\033[102X", "6.1-2", [ 6, 1, 2 ], 29, 26, "position",
|
||
|
|
"X79975EC6783B4293" ],
|
||
|
|
[ "\033[2XPosInParent\033[102X", "6.1-3", [ 6, 1, 3 ], 48, 27,
|
||
|
|
"posinparent", "X832295DE866E44EE" ],
|
||
|
|
[ "\033[2XSubquasigroup\033[102X", "6.2-1", [ 6, 2, 1 ], 65, 27,
|
||
|
|
"subquasigroup", "X7DD511FF864FCDFF" ],
|
||
|
|
[ "\033[2XSubloop\033[102X", "6.2-2", [ 6, 2, 2 ], 84, 27, "subloop",
|
||
|
|
"X84E6744E804AE830" ],
|
||
|
|
[ "\033[2XIsSubquasigroup\033[102X", "6.2-3", [ 6, 2, 3 ], 93, 27,
|
||
|
|
"issubquasigroup", "X87AC8B7E80CE9260" ],
|
||
|
|
[ "\033[2XIsSubloop\033[102X", "6.2-3", [ 6, 2, 3 ], 93, 27, "issubloop",
|
||
|
|
"X87AC8B7E80CE9260" ],
|
||
|
|
[ "\033[2XAllSubquasigroups\033[102X", "6.2-4", [ 6, 2, 4 ], 103, 27,
|
||
|
|
"allsubquasigroups", "X859B6C8183537E75" ],
|
||
|
|
[ "\033[2XAllSubloops\033[102X", "6.2-5", [ 6, 2, 5 ], 108, 28,
|
||
|
|
"allsubloops", "X81EF252585592001" ],
|
||
|
|
[ "\033[2XRightCosets\033[102X", "6.2-6", [ 6, 2, 6 ], 113, 28,
|
||
|
|
"rightcosets", "X835F48248571364F" ],
|
||
|
|
[ "coset", "6.2-6", [ 6, 2, 6 ], 113, 28, "coset", "X835F48248571364F" ],
|
||
|
|
[ "\033[2XRightTransversal\033[102X", "6.2-7", [ 6, 2, 7 ], 123, 28,
|
||
|
|
"righttransversal", "X85C65D06822E716F" ],
|
||
|
|
[ "transversal", "6.2-7", [ 6, 2, 7 ], 123, 28, "transversal",
|
||
|
|
"X85C65D06822E716F" ],
|
||
|
|
[ "\033[2XLeftTranslation\033[102X", "6.3-1", [ 6, 3, 1 ], 143, 28,
|
||
|
|
"lefttranslation", "X7B45B48C7C4D6061" ],
|
||
|
|
[ "\033[2XRightTranslation\033[102X", "6.3-1", [ 6, 3, 1 ], 143, 28,
|
||
|
|
"righttranslation", "X7B45B48C7C4D6061" ],
|
||
|
|
[ "\033[2XLeftSection\033[102X", "6.3-2", [ 6, 3, 2 ], 151, 28,
|
||
|
|
"leftsection", "X7EB9197C80FB4664" ],
|
||
|
|
[ "\033[2XRightSection\033[102X", "6.3-2", [ 6, 3, 2 ], 151, 28,
|
||
|
|
"rightsection", "X7EB9197C80FB4664" ],
|
||
|
|
[ "\033[2XLeftMultiplicationGroup\033[102X", "6.4-1", [ 6, 4, 1 ], 193, 29,
|
||
|
|
"leftmultiplicationgroup", "X87302BE983A5FC61" ],
|
||
|
|
[ "\033[2XRightMultiplicationGroup\033[102X", "6.4-1", [ 6, 4, 1 ], 193,
|
||
|
|
29, "rightmultiplicationgroup", "X87302BE983A5FC61" ],
|
||
|
|
[ "\033[2XMultiplicationGroup\033[102X", "6.4-1", [ 6, 4, 1 ], 193, 29,
|
||
|
|
"multiplicationgroup", "X87302BE983A5FC61" ],
|
||
|
|
[ "\033[2XRelativeLeftMultiplicationGroup\033[102X", "6.4-2", [ 6, 4, 2 ],
|
||
|
|
203, 29, "relativeleftmultiplicationgroup", "X847256B779E1E7E5" ],
|
||
|
|
[ "\033[2XRelativeRightMultiplicationGroup\033[102X", "6.4-2", [ 6, 4, 2 ],
|
||
|
|
203, 29, "relativerightmultiplicationgroup", "X847256B779E1E7E5" ],
|
||
|
|
[ "\033[2XRelativeMultiplicationGroup\033[102X", "6.4-2", [ 6, 4, 2 ], 203,
|
||
|
|
29, "relativemultiplicationgroup", "X847256B779E1E7E5" ],
|
||
|
|
[ "multiplication group relative left", "6.4-2", [ 6, 4, 2 ], 203, 29,
|
||
|
|
"multiplication group relative left", "X847256B779E1E7E5" ],
|
||
|
|
[ "multiplication group relative right ", "6.4-2", [ 6, 4, 2 ], 203, 29,
|
||
|
|
"multiplication group relative right", "X847256B779E1E7E5" ],
|
||
|
|
[ "multiplication group relative", "6.4-2", [ 6, 4, 2 ], 203, 29,
|
||
|
|
"multiplication group relative", "X847256B779E1E7E5" ],
|
||
|
|
[ "inner mapping left", "6.5", [ 6, 5, 0 ], 220, 29, "inner mapping left",
|
||
|
|
"X8740D61178ACD217" ],
|
||
|
|
[ "inner mapping right", "6.5", [ 6, 5, 0 ], 220, 29, "inner mapping right",
|
||
|
|
"X8740D61178ACD217" ],
|
||
|
|
[ "conjugation", "6.5", [ 6, 5, 0 ], 220, 29, "conjugation",
|
||
|
|
"X8740D61178ACD217" ],
|
||
|
|
[ "inner mapping middle", "6.5", [ 6, 5, 0 ], 220, 29,
|
||
|
|
"inner mapping middle", "X8740D61178ACD217" ],
|
||
|
|
[ "inner mapping group middle", "6.5", [ 6, 5, 0 ], 220, 29,
|
||
|
|
"inner mapping group middle", "X8740D61178ACD217" ],
|
||
|
|
[ "\033[2XLeftInnerMapping\033[102X", "6.5-1", [ 6, 5, 1 ], 231, 30,
|
||
|
|
"leftinnermapping", "X7EE1E78C856C6F7C" ],
|
||
|
|
[ "\033[2XRightInnerMapping\033[102X", "6.5-1", [ 6, 5, 1 ], 231, 30,
|
||
|
|
"rightinnermapping", "X7EE1E78C856C6F7C" ],
|
||
|
|
[ "\033[2XMiddleInnerMapping\033[102X", "6.5-1", [ 6, 5, 1 ], 231, 30,
|
||
|
|
"middleinnermapping", "X7EE1E78C856C6F7C" ],
|
||
|
|
[ "\033[2XLeftInnerMappingGroup\033[102X", "6.5-2", [ 6, 5, 2 ], 240, 30,
|
||
|
|
"leftinnermappinggroup", "X79CDA09A7D48BF2B" ],
|
||
|
|
[ "\033[2XRightInnerMappingGroup\033[102X", "6.5-2", [ 6, 5, 2 ], 240, 30,
|
||
|
|
"rightinnermappinggroup", "X79CDA09A7D48BF2B" ],
|
||
|
|
[ "\033[2XMiddleInnerMappingGroup\033[102X", "6.5-2", [ 6, 5, 2 ], 240, 30,
|
||
|
|
"middleinnermappinggroup", "X79CDA09A7D48BF2B" ],
|
||
|
|
[ "\033[2XInnerMappingGroup\033[102X", "6.5-3", [ 6, 5, 3 ], 249, 30,
|
||
|
|
"innermappinggroup", "X82513A3B7C3A6420" ],
|
||
|
|
[ "\033[2XLeftNucleus\033[102X", "6.6-1", [ 6, 6, 1 ], 273, 30,
|
||
|
|
"leftnucleus", "X7DF536FC85BBD1D2" ],
|
||
|
|
[ "\033[2XMiddleNucleus\033[102X", "6.6-1", [ 6, 6, 1 ], 273, 30,
|
||
|
|
"middlenucleus", "X7DF536FC85BBD1D2" ],
|
||
|
|
[ "\033[2XRightNucleus\033[102X", "6.6-1", [ 6, 6, 1 ], 273, 30,
|
||
|
|
"rightnucleus", "X7DF536FC85BBD1D2" ],
|
||
|
|
[ "\033[2XNuc\033[102X", "6.6-2", [ 6, 6, 2 ], 282, 31, "nuc",
|
||
|
|
"X84D389677A91C290" ],
|
||
|
|
[ "\033[2XNucleusOfQuasigroup\033[102X", "6.6-2", [ 6, 6, 2 ], 282, 31,
|
||
|
|
"nucleusofquasigroup", "X84D389677A91C290" ],
|
||
|
|
[ "\033[2XNucleusOfLoop\033[102X", "6.6-2", [ 6, 6, 2 ], 282, 31,
|
||
|
|
"nucleusofloop", "X84D389677A91C290" ],
|
||
|
|
[ "\033[2XCommutant\033[102X", "6.6-3", [ 6, 6, 3 ], 298, 31, "commutant",
|
||
|
|
"X7C8428DE791F3CE1" ],
|
||
|
|
[ "\033[2XCenter\033[102X", "6.6-4", [ 6, 6, 4 ], 303, 31, "center",
|
||
|
|
"X7C1FBE7A84DD4873" ],
|
||
|
|
[ "\033[2XAssociatorSubloop\033[102X", "6.6-5", [ 6, 6, 5 ], 311, 31,
|
||
|
|
"associatorsubloop", "X7F7FDE82780EDD7E" ],
|
||
|
|
[ "\033[2XIsNormal\033[102X", "6.7-1", [ 6, 7, 1 ], 323, 31, "isnormal",
|
||
|
|
"X838186F9836F678C" ],
|
||
|
|
[ "subloop normal", "6.7-1", [ 6, 7, 1 ], 323, 31, "subloop normal",
|
||
|
|
"X838186F9836F678C" ],
|
||
|
|
[ "normal subloop", "6.7-1", [ 6, 7, 1 ], 323, 31, "normal subloop",
|
||
|
|
"X838186F9836F678C" ],
|
||
|
|
[ "\033[2XNormalClosure\033[102X", "6.7-2", [ 6, 7, 2 ], 331, 31,
|
||
|
|
"normalclosure", "X7BDEA0A98720D1BB" ],
|
||
|
|
[ "normal closure", "6.7-2", [ 6, 7, 2 ], 331, 31, "normal closure",
|
||
|
|
"X7BDEA0A98720D1BB" ],
|
||
|
|
[ "\033[2XIsSimple\033[102X", "6.7-3", [ 6, 7, 3 ], 339, 32, "issimple",
|
||
|
|
"X7D8E63A7824037CC" ],
|
||
|
|
[ "simple loop", "6.7-3", [ 6, 7, 3 ], 339, 32, "simple loop",
|
||
|
|
"X7D8E63A7824037CC" ],
|
||
|
|
[ "loop simple", "6.7-3", [ 6, 7, 3 ], 339, 32, "loop simple",
|
||
|
|
"X7D8E63A7824037CC" ],
|
||
|
|
[ "\033[2XFactorLoop\033[102X", "6.8-1", [ 6, 8, 1 ], 349, 32,
|
||
|
|
"factorloop", "X83E1953980E2DE2F" ],
|
||
|
|
[ "\033[2XNaturalHomomorphismByNormalSubloop\033[102X", "6.8-2",
|
||
|
|
[ 6, 8, 2 ], 355, 32, "naturalhomomorphismbynormalsubloop",
|
||
|
|
"X870FCB497AECC730" ],
|
||
|
|
[ "\033[2XIsNilpotent\033[102X", "6.9-1", [ 6, 9, 1 ], 378, 32,
|
||
|
|
"isnilpotent", "X78A4B93781C96AAE" ],
|
||
|
|
[ "\033[2XNilpotencyClassOfLoop\033[102X", "6.9-2", [ 6, 9, 2 ], 383, 32,
|
||
|
|
"nilpotencyclassofloop", "X7D5FC62581A99482" ],
|
||
|
|
[ "\033[2XIsStronglyNilpotent\033[102X", "6.9-3", [ 6, 9, 3 ], 389, 32,
|
||
|
|
"isstronglynilpotent", "X7E7C2D117B55F6A0" ],
|
||
|
|
[ "strongly nilpotent loop", "6.9-3", [ 6, 9, 3 ], 389, 32,
|
||
|
|
"strongly nilpotent loop", "X7E7C2D117B55F6A0" ],
|
||
|
|
[ "nilpotent loop strongly", "6.9-3", [ 6, 9, 3 ], 389, 32,
|
||
|
|
"nilpotent loop strongly", "X7E7C2D117B55F6A0" ],
|
||
|
|
[ "loop strongly nilpotent", "6.9-3", [ 6, 9, 3 ], 389, 32,
|
||
|
|
"loop strongly nilpotent", "X7E7C2D117B55F6A0" ],
|
||
|
|
[ "\033[2XUpperCentralSeries\033[102X", "6.9-4", [ 6, 9, 4 ], 397, 33,
|
||
|
|
"uppercentralseries", "X7ED37AA07BEE79E0" ],
|
||
|
|
[ "\033[2XLowerCentralSeries\033[102X", "6.9-5", [ 6, 9, 5 ], 403, 33,
|
||
|
|
"lowercentralseries", "X817BDBC2812992ED" ],
|
||
|
|
[ "central series lower", "6.9-5", [ 6, 9, 5 ], 403, 33,
|
||
|
|
"central series lower", "X817BDBC2812992ED" ],
|
||
|
|
[ "\033[2XIsSolvable\033[102X", "6.10-1", [ 6, 10, 1 ], 416, 33,
|
||
|
|
"issolvable", "X79B10B337A3B1C6E" ],
|
||
|
|
[ "\033[2XDerivedSubloop\033[102X", "6.10-2", [ 6, 10, 2 ], 421, 33,
|
||
|
|
"derivedsubloop", "X7A82DC4680DAD67C" ],
|
||
|
|
[ "\033[2XDerivedLength\033[102X", "6.10-3", [ 6, 10, 3 ], 426, 33,
|
||
|
|
"derivedlength", "X7A9AA1577CEC891F" ],
|
||
|
|
[ "\033[2XFrattiniSubloop\033[102X", "6.10-4", [ 6, 10, 4 ], 432, 33,
|
||
|
|
"frattinisubloop", "X85BD2C517FA7A47E" ],
|
||
|
|
[ "Frattini subloop", "6.10-4", [ 6, 10, 4 ], 432, 33, "frattini subloop",
|
||
|
|
"X85BD2C517FA7A47E" ],
|
||
|
|
[ "\033[2XFrattinifactorSize\033[102X", "6.10-5", [ 6, 10, 5 ], 441, 33,
|
||
|
|
"frattinifactorsize", "X855286367A2D5A54" ],
|
||
|
|
[ "\033[2XIsomorphismQuasigroups\033[102X", "6.11-1", [ 6, 11, 1 ], 447,
|
||
|
|
33, "isomorphismquasigroups", "X801067F67E5292F7" ],
|
||
|
|
[ "\033[2XIsomorphismLoops\033[102X", "6.11-2", [ 6, 11, 2 ], 458, 34,
|
||
|
|
"isomorphismloops", "X7D7B10D6836FCA9F" ],
|
||
|
|
[ "\033[2XQuasigroupsUpToIsomorphism\033[102X", "6.11-3", [ 6, 11, 3 ],
|
||
|
|
465, 34, "quasigroupsuptoisomorphism", "X82373C5479574F22" ],
|
||
|
|
[ "\033[2XLoopsUpToIsomorphism\033[102X", "6.11-4", [ 6, 11, 4 ], 471, 34,
|
||
|
|
"loopsuptoisomorphism", "X8308F38283C61B20" ],
|
||
|
|
[ "\033[2XAutomorphismGroup\033[102X", "6.11-5", [ 6, 11, 5 ], 477, 34,
|
||
|
|
"automorphismgroup", "X87677B0787B4461A" ],
|
||
|
|
[ "\033[2XIsomorphicCopyByPerm\033[102X", "6.11-6", [ 6, 11, 6 ], 491, 34,
|
||
|
|
"isomorphiccopybyperm", "X85B3E22679FD8D81" ],
|
||
|
|
[ "\033[2XIsomorphicCopyByNormalSubloop\033[102X", "6.11-7", [ 6, 11, 7 ],
|
||
|
|
501, 34, "isomorphiccopybynormalsubloop", "X8121DE3A78795040" ],
|
||
|
|
[ "\033[2XDiscriminator\033[102X", "6.11-8", [ 6, 11, 8 ], 514, 35,
|
||
|
|
"discriminator", "X7D09D8957E4A0973" ],
|
||
|
|
[ "\033[2XAreEqualDiscriminators\033[102X", "6.11-9", [ 6, 11, 9 ], 526,
|
||
|
|
35, "areequaldiscriminators", "X812F0DEE7C896E18" ],
|
||
|
|
[ "\033[2XIsotopismLoops\033[102X", "6.12-1", [ 6, 12, 1 ], 542, 35,
|
||
|
|
"isotopismloops", "X84C5ADE77F910F63" ],
|
||
|
|
[ "\033[2XLoopsUpToIsotopism\033[102X", "6.12-2", [ 6, 12, 2 ], 548, 35,
|
||
|
|
"loopsuptoisotopism", "X841E540B7A7EF29F" ],
|
||
|
|
[ "\033[2XIsAssociative\033[102X", "7.1-1", [ 7, 1, 1 ], 19, 36,
|
||
|
|
"isassociative", "X7C83B5A47FD18FB7" ],
|
||
|
|
[ "\033[2XIsCommutative\033[102X", "7.1-2", [ 7, 1, 2 ], 24, 36,
|
||
|
|
"iscommutative", "X830A4A4C795FBC2D" ],
|
||
|
|
[ "\033[2XIsPowerAssociative\033[102X", "7.1-3", [ 7, 1, 3 ], 29, 36,
|
||
|
|
"ispowerassociative", "X7D53EA947F1CDA69" ],
|
||
|
|
[ "quasigroup power associative", "7.1-3", [ 7, 1, 3 ], 29, 36,
|
||
|
|
"quasigroup power associative", "X7D53EA947F1CDA69" ],
|
||
|
|
[ "power associative quasigroup", "7.1-3", [ 7, 1, 3 ], 29, 36,
|
||
|
|
"power associative quasigroup", "X7D53EA947F1CDA69" ],
|
||
|
|
[ "\033[2XIsDiassociative\033[102X", "7.1-4", [ 7, 1, 4 ], 37, 36,
|
||
|
|
"isdiassociative", "X872DCA027E1A4A1D" ],
|
||
|
|
[ "quasigroup diassociative", "7.1-4", [ 7, 1, 4 ], 37, 36,
|
||
|
|
"quasigroup diassociative", "X872DCA027E1A4A1D" ],
|
||
|
|
[ "diassociative quasigroup", "7.1-4", [ 7, 1, 4 ], 37, 36,
|
||
|
|
"diassociative quasigroup", "X872DCA027E1A4A1D" ],
|
||
|
|
[ "inverse left", "7.2", [ 7, 2, 0 ], 46, 37, "inverse left",
|
||
|
|
"X853841C5820BFEA4" ],
|
||
|
|
[ "inverse right", "7.2", [ 7, 2, 0 ], 46, 37, "inverse right",
|
||
|
|
"X853841C5820BFEA4" ],
|
||
|
|
[ "\033[2XHasLeftInverseProperty\033[102X", "7.2-1", [ 7, 2, 1 ], 53, 37,
|
||
|
|
"hasleftinverseproperty", "X85EDD10586596458" ],
|
||
|
|
[ "\033[2XHasRightInverseProperty\033[102X", "7.2-1", [ 7, 2, 1 ], 53, 37,
|
||
|
|
"hasrightinverseproperty", "X85EDD10586596458" ],
|
||
|
|
[ "\033[2XHasInverseProperty\033[102X", "7.2-1", [ 7, 2, 1 ], 53, 37,
|
||
|
|
"hasinverseproperty", "X85EDD10586596458" ],
|
||
|
|
[ "inverse property left", "7.2-1", [ 7, 2, 1 ], 53, 37,
|
||
|
|
"inverse property left", "X85EDD10586596458" ],
|
||
|
|
[ "inverse property right", "7.2-1", [ 7, 2, 1 ], 53, 37,
|
||
|
|
"inverse property right", "X85EDD10586596458" ],
|
||
|
|
[ "inverse property", "7.2-1", [ 7, 2, 1 ], 53, 37, "inverse property",
|
||
|
|
"X85EDD10586596458" ],
|
||
|
|
[ "\033[2XHasTwosidedInverses\033[102X", "7.2-2", [ 7, 2, 2 ], 67, 37,
|
||
|
|
"hastwosidedinverses", "X86B93E1B7AEA6EDA" ],
|
||
|
|
[ "inverse two-sided", "7.2-2", [ 7, 2, 2 ], 67, 37, "inverse two-sided",
|
||
|
|
"X86B93E1B7AEA6EDA" ],
|
||
|
|
[ "\033[2XHasWeakInverseProperty\033[102X", "7.2-3", [ 7, 2, 3 ], 74, 37,
|
||
|
|
"hasweakinverseproperty", "X793909B780761EA8" ],
|
||
|
|
[ "inverse property weak", "7.2-3", [ 7, 2, 3 ], 74, 37,
|
||
|
|
"inverse property weak", "X793909B780761EA8" ],
|
||
|
|
[ "\033[2XHasAutomorphicInverseProperty\033[102X", "7.2-4", [ 7, 2, 4 ],
|
||
|
|
82, 37, "hasautomorphicinverseproperty", "X7F46CE6B7D387158" ],
|
||
|
|
[ "automorphic inverse property", "7.2-4", [ 7, 2, 4 ], 82, 37,
|
||
|
|
"automorphic inverse property", "X7F46CE6B7D387158" ],
|
||
|
|
[ "inverse property automorphic", "7.2-4", [ 7, 2, 4 ], 82, 37,
|
||
|
|
"inverse property automorphic", "X7F46CE6B7D387158" ],
|
||
|
|
[ "\033[2XHasAntiautomorphicInverseProperty\033[102X", "7.2-5",
|
||
|
|
[ 7, 2, 5 ], 91, 37, "hasantiautomorphicinverseproperty",
|
||
|
|
"X8538D4638232DB51" ],
|
||
|
|
[ "antiautomorphic inverse property", "7.2-5", [ 7, 2, 5 ], 91, 37,
|
||
|
|
"antiautomorphic inverse property", "X8538D4638232DB51" ],
|
||
|
|
[ "inverse property antiautomorphic", "7.2-5", [ 7, 2, 5 ], 91, 37,
|
||
|
|
"inverse property antiautomorphic", "X8538D4638232DB51" ],
|
||
|
|
[ "\033[2XIsSemisymmetric\033[102X", "7.3-1", [ 7, 3, 1 ], 105, 38,
|
||
|
|
"issemisymmetric", "X834848ED85F9012B" ],
|
||
|
|
[ "semisymmetric quasigroup", "7.3-1", [ 7, 3, 1 ], 105, 38,
|
||
|
|
"semisymmetric quasigroup", "X834848ED85F9012B" ],
|
||
|
|
[ "quasigroup semisymmetric", "7.3-1", [ 7, 3, 1 ], 105, 38,
|
||
|
|
"quasigroup semisymmetric", "X834848ED85F9012B" ],
|
||
|
|
[ "\033[2XIsTotallySymmetric\033[102X", "7.3-2", [ 7, 3, 2 ], 113, 38,
|
||
|
|
"istotallysymmetric", "X834F809B8060B754" ],
|
||
|
|
[ "totally symmetric quasigroup", "7.3-2", [ 7, 3, 2 ], 113, 38,
|
||
|
|
"totally symmetric quasigroup", "X834F809B8060B754" ],
|
||
|
|
[ "quasigroup totally symmetric", "7.3-2", [ 7, 3, 2 ], 113, 38,
|
||
|
|
"quasigroup totally symmetric", "X834F809B8060B754" ],
|
||
|
|
[ "\033[2XIsIdempotent\033[102X", "7.3-3", [ 7, 3, 3 ], 122, 38,
|
||
|
|
"isidempotent", "X7CB5896082D29173" ],
|
||
|
|
[ "idempotent quasigroup", "7.3-3", [ 7, 3, 3 ], 122, 38,
|
||
|
|
"idempotent quasigroup", "X7CB5896082D29173" ],
|
||
|
|
[ "quasigroup idempotent", "7.3-3", [ 7, 3, 3 ], 122, 38,
|
||
|
|
"quasigroup idempotent", "X7CB5896082D29173" ],
|
||
|
|
[ "\033[2XIsSteinerQuasigroup\033[102X", "7.3-4", [ 7, 3, 4 ], 129, 38,
|
||
|
|
"issteinerquasigroup", "X83DE7DD77C056C1F" ],
|
||
|
|
[ "Steiner quasigroup", "7.3-4", [ 7, 3, 4 ], 129, 38, "steiner quasigroup",
|
||
|
|
"X83DE7DD77C056C1F" ],
|
||
|
|
[ "quasigroup Steiner", "7.3-4", [ 7, 3, 4 ], 129, 38, "quasigroup steiner",
|
||
|
|
"X83DE7DD77C056C1F" ],
|
||
|
|
[ "unipotent quasigroup", "7.3-5", [ 7, 3, 5 ], 136, 38,
|
||
|
|
"unipotent quasigroup", "X7CA3DCA07B6CB9BD" ],
|
||
|
|
[ "quasigroup unipotent", "7.3-5", [ 7, 3, 5 ], 136, 38,
|
||
|
|
"quasigroup unipotent", "X7CA3DCA07B6CB9BD" ],
|
||
|
|
[ "\033[2XIsUnipotent\033[102X", "7.3-5", [ 7, 3, 5 ], 136, 38,
|
||
|
|
"isunipotent", "X7CA3DCA07B6CB9BD" ],
|
||
|
|
[ "\033[2XIsLeftDistributive\033[102X", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"isleftdistributive", "X7B76FD6E878ED4F1" ],
|
||
|
|
[ "\033[2XIsRightDistributive\033[102X", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"isrightdistributive", "X7B76FD6E878ED4F1" ],
|
||
|
|
[ "\033[2XIsDistributive\033[102X", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"isdistributive", "X7B76FD6E878ED4F1" ],
|
||
|
|
[ "quasigroup left distributive", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"quasigroup left distributive", "X7B76FD6E878ED4F1" ],
|
||
|
|
[ "distributive quasigroup left", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"distributive quasigroup left", "X7B76FD6E878ED4F1" ],
|
||
|
|
[ "quasigroup right distributive", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"quasigroup right distributive", "X7B76FD6E878ED4F1" ],
|
||
|
|
[ "distributive quasigroup right", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"distributive quasigroup right", "X7B76FD6E878ED4F1" ],
|
||
|
|
[ "quasigroup distributive", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"quasigroup distributive", "X7B76FD6E878ED4F1" ],
|
||
|
|
[ "distributive quasigroup", "7.3-6", [ 7, 3, 6 ], 143, 38,
|
||
|
|
"distributive quasigroup", "X7B76FD6E878ED4F1" ],
|
||
|
|
[ "\033[2XIsEntropic\033[102X", "7.3-7", [ 7, 3, 7 ], 160, 39,
|
||
|
|
"isentropic", "X7F23D4D97A38D223" ],
|
||
|
|
[ "\033[2XIsMedial\033[102X", "7.3-7", [ 7, 3, 7 ], 160, 39, "ismedial",
|
||
|
|
"X7F23D4D97A38D223" ],
|
||
|
|
[ "entropic quasigroup", "7.3-7", [ 7, 3, 7 ], 160, 39,
|
||
|
|
"entropic quasigroup", "X7F23D4D97A38D223" ],
|
||
|
|
[ "quasigroup entropic", "7.3-7", [ 7, 3, 7 ], 160, 39,
|
||
|
|
"quasigroup entropic", "X7F23D4D97A38D223" ],
|
||
|
|
[ "medial quasigroup", "7.3-7", [ 7, 3, 7 ], 160, 39, "medial quasigroup",
|
||
|
|
"X7F23D4D97A38D223" ],
|
||
|
|
[ "quasigroup medial", "7.3-7", [ 7, 3, 7 ], 160, 39, "quasigroup medial",
|
||
|
|
"X7F23D4D97A38D223" ],
|
||
|
|
[ "loop of Bol-Moufang type", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"loop of bol-moufang type", "X780D907986EBA6C7" ],
|
||
|
|
[ "identity of Bol-Moufang type", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"identity of bol-moufang type", "X780D907986EBA6C7" ],
|
||
|
|
[ "alternative loop left", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"alternative loop left", "X780D907986EBA6C7" ],
|
||
|
|
[ "loop left alternative", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"loop left alternative", "X780D907986EBA6C7" ],
|
||
|
|
[ "alternative loop right", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"alternative loop right", "X780D907986EBA6C7" ],
|
||
|
|
[ "loop right alternative", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"loop right alternative", "X780D907986EBA6C7" ],
|
||
|
|
[ "nuclear square loop left", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"nuclear square loop left", "X780D907986EBA6C7" ],
|
||
|
|
[ "loop left nuclear square", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"loop left nuclear square", "X780D907986EBA6C7" ],
|
||
|
|
[ "nuclear square loop middle", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"nuclear square loop middle", "X780D907986EBA6C7" ],
|
||
|
|
[ "loop middle nuclear square", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"loop middle nuclear square", "X780D907986EBA6C7" ],
|
||
|
|
[ "nuclear square loop right", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"nuclear square loop right", "X780D907986EBA6C7" ],
|
||
|
|
[ "loop right nuclear square", "7.4", [ 7, 4, 0 ], 170, 39,
|
||
|
|
"loop right nuclear square", "X780D907986EBA6C7" ],
|
||
|
|
[ "flexible loop", "7.4", [ 7, 4, 0 ], 170, 39, "flexible loop",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "loop flexible", "7.4", [ 7, 4, 0 ], 170, 39, "loop flexible",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "Bol loop left", "7.4", [ 7, 4, 0 ], 170, 39, "bol loop left",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "loop left Bol", "7.4", [ 7, 4, 0 ], 170, 39, "loop left bol",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "Bol loop right", "7.4", [ 7, 4, 0 ], 170, 39, "bol loop right",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "loop right Bol", "7.4", [ 7, 4, 0 ], 170, 39, "loop right bol",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "LC loop", "7.4", [ 7, 4, 0 ], 170, 39, "lc loop", "X780D907986EBA6C7" ],
|
||
|
|
[ "loop LC", "7.4", [ 7, 4, 0 ], 170, 39, "loop lc", "X780D907986EBA6C7" ],
|
||
|
|
[ "RC loop", "7.4", [ 7, 4, 0 ], 170, 39, "rc loop", "X780D907986EBA6C7" ],
|
||
|
|
[ "loop RC", "7.4", [ 7, 4, 0 ], 170, 39, "loop rc", "X780D907986EBA6C7" ],
|
||
|
|
[ "Moufang loop", "7.4", [ 7, 4, 0 ], 170, 39, "moufang loop",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "loop Moufang", "7.4", [ 7, 4, 0 ], 170, 39, "loop moufang",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "C loop", "7.4", [ 7, 4, 0 ], 170, 39, "c loop", "X780D907986EBA6C7" ],
|
||
|
|
[ "loop C", "7.4", [ 7, 4, 0 ], 170, 39, "loop c", "X780D907986EBA6C7" ],
|
||
|
|
[ "extra loop", "7.4", [ 7, 4, 0 ], 170, 39, "extra loop",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "loop extra", "7.4", [ 7, 4, 0 ], 170, 39, "loop extra",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "alternative loop", "7.4", [ 7, 4, 0 ], 170, 39, "alternative loop",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "loop alternative", "7.4", [ 7, 4, 0 ], 170, 39, "loop alternative",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "nuclear square loop", "7.4", [ 7, 4, 0 ], 170, 39, "nuclear square loop",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "loop nuclear square", "7.4", [ 7, 4, 0 ], 170, 39, "loop nuclear square",
|
||
|
|
"X780D907986EBA6C7" ],
|
||
|
|
[ "\033[2XIsExtraLoop\033[102X", "7.4-1", [ 7, 4, 1 ], 223, 40,
|
||
|
|
"isextraloop", "X7988AFE27D06ACB5" ],
|
||
|
|
[ "\033[2XIsMoufangLoop\033[102X", "7.4-2", [ 7, 4, 2 ], 228, 40,
|
||
|
|
"ismoufangloop", "X7F1C151484C97E61" ],
|
||
|
|
[ "\033[2XIsCLoop\033[102X", "7.4-3", [ 7, 4, 3 ], 233, 40, "iscloop",
|
||
|
|
"X866F04DC7AE54B7C" ],
|
||
|
|
[ "\033[2XIsLeftBolLoop\033[102X", "7.4-4", [ 7, 4, 4 ], 238, 40,
|
||
|
|
"isleftbolloop", "X801DAAE8834A1A65" ],
|
||
|
|
[ "\033[2XIsRightBolLoop\033[102X", "7.4-5", [ 7, 4, 5 ], 243, 40,
|
||
|
|
"isrightbolloop", "X79279F9787E72566" ],
|
||
|
|
[ "\033[2XIsLCLoop\033[102X", "7.4-6", [ 7, 4, 6 ], 248, 40, "islcloop",
|
||
|
|
"X789E0A6979697C4C" ],
|
||
|
|
[ "\033[2XIsRCLoop\033[102X", "7.4-7", [ 7, 4, 7 ], 253, 40, "isrcloop",
|
||
|
|
"X7B03CC577802F4AB" ],
|
||
|
|
[ "\033[2XIsLeftNuclearSquareLoop\033[102X", "7.4-8", [ 7, 4, 8 ], 258, 40,
|
||
|
|
"isleftnuclearsquareloop", "X819F285887B5EB9E" ],
|
||
|
|
[ "\033[2XIsMiddleNuclearSquareLoop\033[102X", "7.4-9", [ 7, 4, 9 ], 263,
|
||
|
|
40, "ismiddlenuclearsquareloop", "X8474F55681244A8A" ],
|
||
|
|
[ "\033[2XIsRightNuclearSquareLoop\033[102X", "7.4-10", [ 7, 4, 10 ], 268,
|
||
|
|
40, "isrightnuclearsquareloop", "X807B3B21825E3076" ],
|
||
|
|
[ "\033[2XIsNuclearSquareLoop\033[102X", "7.4-11", [ 7, 4, 11 ], 273, 41,
|
||
|
|
"isnuclearsquareloop", "X796650088213229B" ],
|
||
|
|
[ "\033[2XIsFlexible\033[102X", "7.4-12", [ 7, 4, 12 ], 278, 41,
|
||
|
|
"isflexible", "X7C32851A7AF1C45F" ],
|
||
|
|
[ "\033[2XIsLeftAlternative\033[102X", "7.4-13", [ 7, 4, 13 ], 283, 41,
|
||
|
|
"isleftalternative", "X7DF0196786B9CE08" ],
|
||
|
|
[ "\033[2XIsRightAlternative\033[102X", "7.4-14", [ 7, 4, 14 ], 288, 41,
|
||
|
|
"isrightalternative", "X8416FAD87F148F5D" ],
|
||
|
|
[ "\033[2XIsAlternative\033[102X", "7.4-15", [ 7, 4, 15 ], 293, 41,
|
||
|
|
"isalternative", "X8379356E82DB5DDA" ],
|
||
|
|
[ "power alternative loop left", "7.5", [ 7, 5, 0 ], 324, 42,
|
||
|
|
"power alternative loop left", "X83A501387E1AC371" ],
|
||
|
|
[ "loop left power alternative", "7.5", [ 7, 5, 0 ], 324, 42,
|
||
|
|
"loop left power alternative", "X83A501387E1AC371" ],
|
||
|
|
[ "power alternative loop right", "7.5", [ 7, 5, 0 ], 324, 42,
|
||
|
|
"power alternative loop right", "X83A501387E1AC371" ],
|
||
|
|
[ "loop right power alternative", "7.5", [ 7, 5, 0 ], 324, 42,
|
||
|
|
"loop right power alternative", "X83A501387E1AC371" ],
|
||
|
|
[ "power alternative loop", "7.5", [ 7, 5, 0 ], 324, 42,
|
||
|
|
"power alternative loop", "X83A501387E1AC371" ],
|
||
|
|
[ "loop power alternative", "7.5", [ 7, 5, 0 ], 324, 42,
|
||
|
|
"loop power alternative", "X83A501387E1AC371" ],
|
||
|
|
[ "\033[2XIsLeftPowerAlternative\033[102X", "7.5-1", [ 7, 5, 1 ], 337, 42,
|
||
|
|
"isleftpoweralternative", "X875C3DF681B3FAE2" ],
|
||
|
|
[ "\033[2XIsRightPowerAlternative\033[102X", "7.5-1", [ 7, 5, 1 ], 337, 42,
|
||
|
|
"isrightpoweralternative", "X875C3DF681B3FAE2" ],
|
||
|
|
[ "\033[2XIsPowerAlternative\033[102X", "7.5-1", [ 7, 5, 1 ], 337, 42,
|
||
|
|
"ispoweralternative", "X875C3DF681B3FAE2" ],
|
||
|
|
[ "conjugacy closed loop left", "7.6", [ 7, 6, 0 ], 346, 42,
|
||
|
|
"conjugacy closed loop left", "X8176B2C47A4629CD" ],
|
||
|
|
[ "loop left conjugacy closed", "7.6", [ 7, 6, 0 ], 346, 42,
|
||
|
|
"loop left conjugacy closed", "X8176B2C47A4629CD" ],
|
||
|
|
[ "conjugacy closed loop right", "7.6", [ 7, 6, 0 ], 346, 42,
|
||
|
|
"conjugacy closed loop right", "X8176B2C47A4629CD" ],
|
||
|
|
[ "loop right conjugacy closed", "7.6", [ 7, 6, 0 ], 346, 42,
|
||
|
|
"loop right conjugacy closed", "X8176B2C47A4629CD" ],
|
||
|
|
[ "conjugacy closed loop", "7.6", [ 7, 6, 0 ], 346, 42,
|
||
|
|
"conjugacy closed loop", "X8176B2C47A4629CD" ],
|
||
|
|
[ "loop conjugacy closed", "7.6", [ 7, 6, 0 ], 346, 42,
|
||
|
|
"loop conjugacy closed", "X8176B2C47A4629CD" ],
|
||
|
|
[ "\033[2XIsLCCLoop\033[102X", "7.6-1", [ 7, 6, 1 ], 358, 42, "islccloop",
|
||
|
|
"X784E08CD7B710AF4" ],
|
||
|
|
[ "\033[2XIsLeftConjugacyClosedLoop\033[102X", "7.6-1", [ 7, 6, 1 ], 358,
|
||
|
|
42, "isleftconjugacyclosedloop", "X784E08CD7B710AF4" ],
|
||
|
|
[ "\033[2XIsRCCLoop\033[102X", "7.6-2", [ 7, 6, 2 ], 364, 42, "isrccloop",
|
||
|
|
"X7B3016B47A1A8213" ],
|
||
|
|
[ "\033[2XIsRightConjugacyClosedLoop\033[102X", "7.6-2", [ 7, 6, 2 ], 364,
|
||
|
|
42, "isrightconjugacyclosedloop", "X7B3016B47A1A8213" ],
|
||
|
|
[ "\033[2XIsCCLoop\033[102X", "7.6-3", [ 7, 6, 3 ], 370, 42, "isccloop",
|
||
|
|
"X878B614479DCB83F" ],
|
||
|
|
[ "\033[2XIsConjugacyClosedLoop\033[102X", "7.6-3", [ 7, 6, 3 ], 370, 42,
|
||
|
|
"isconjugacyclosedloop", "X878B614479DCB83F" ],
|
||
|
|
[ "\033[2XIsOsbornLoop\033[102X", "7.6-4", [ 7, 6, 4 ], 376, 42,
|
||
|
|
"isosbornloop", "X8655956878205FC1" ],
|
||
|
|
[ "Osborn loop", "7.6-4", [ 7, 6, 4 ], 376, 42, "osborn loop",
|
||
|
|
"X8655956878205FC1" ],
|
||
|
|
[ "loop Osborn", "7.6-4", [ 7, 6, 4 ], 376, 42, "loop osborn",
|
||
|
|
"X8655956878205FC1" ],
|
||
|
|
[ "automorphic loop left", "7.7", [ 7, 7, 0 ], 384, 43,
|
||
|
|
"automorphic loop left", "X793B22EA8643C667" ],
|
||
|
|
[ "loop left automorphic", "7.7", [ 7, 7, 0 ], 384, 43,
|
||
|
|
"loop left automorphic", "X793B22EA8643C667" ],
|
||
|
|
[ "automorphic loop middle", "7.7", [ 7, 7, 0 ], 384, 43,
|
||
|
|
"automorphic loop middle", "X793B22EA8643C667" ],
|
||
|
|
[ "loop middle automorphic", "7.7", [ 7, 7, 0 ], 384, 43,
|
||
|
|
"loop middle automorphic", "X793B22EA8643C667" ],
|
||
|
|
[ "automorphic loop right", "7.7", [ 7, 7, 0 ], 384, 43,
|
||
|
|
"automorphic loop right", "X793B22EA8643C667" ],
|
||
|
|
[ "loop right automorphic", "7.7", [ 7, 7, 0 ], 384, 43,
|
||
|
|
"loop right automorphic", "X793B22EA8643C667" ],
|
||
|
|
[ "automorphic loop", "7.7", [ 7, 7, 0 ], 384, 43, "automorphic loop",
|
||
|
|
"X793B22EA8643C667" ],
|
||
|
|
[ "loop automorphic", "7.7", [ 7, 7, 0 ], 384, 43, "loop automorphic",
|
||
|
|
"X793B22EA8643C667" ],
|
||
|
|
[ "\033[2XIsLeftAutomorphicLoop\033[102X", "7.7-1", [ 7, 7, 1 ], 425, 43,
|
||
|
|
"isleftautomorphicloop", "X7F063914804659F1" ],
|
||
|
|
[ "\033[2XIsLeftALoop\033[102X", "7.7-1", [ 7, 7, 1 ], 425, 43,
|
||
|
|
"isleftaloop", "X7F063914804659F1" ],
|
||
|
|
[ "\033[2XIsMiddleAutomorphicLoop\033[102X", "7.7-2", [ 7, 7, 2 ], 431, 43,
|
||
|
|
"ismiddleautomorphicloop", "X7DFE830584A769E5" ],
|
||
|
|
[ "\033[2XIsMiddleALoop\033[102X", "7.7-2", [ 7, 7, 2 ], 431, 43,
|
||
|
|
"ismiddlealoop", "X7DFE830584A769E5" ],
|
||
|
|
[ "\033[2XIsRightAutomorphicLoop\033[102X", "7.7-3", [ 7, 7, 3 ], 437, 44,
|
||
|
|
"isrightautomorphicloop", "X7EA9165A87F99E35" ],
|
||
|
|
[ "\033[2XIsRightALoop\033[102X", "7.7-3", [ 7, 7, 3 ], 437, 44,
|
||
|
|
"isrightaloop", "X7EA9165A87F99E35" ],
|
||
|
|
[ "\033[2XIsAutomorphicLoop\033[102X", "7.7-4", [ 7, 7, 4 ], 443, 44,
|
||
|
|
"isautomorphicloop", "X7899603184CF13FD" ],
|
||
|
|
[ "\033[2XIsALoop\033[102X", "7.7-4", [ 7, 7, 4 ], 443, 44, "isaloop",
|
||
|
|
"X7899603184CF13FD" ],
|
||
|
|
[ "\033[2XIsCodeLoop\033[102X", "7.8-1", [ 7, 8, 1 ], 454, 44,
|
||
|
|
"iscodeloop", "X790FA1188087D5C1" ],
|
||
|
|
[ "code loop", "7.8-1", [ 7, 8, 1 ], 454, 44, "code loop",
|
||
|
|
"X790FA1188087D5C1" ],
|
||
|
|
[ "loop code", "7.8-1", [ 7, 8, 1 ], 454, 44, "loop code",
|
||
|
|
"X790FA1188087D5C1" ],
|
||
|
|
[ "\033[2XIsSteinerLoop\033[102X", "7.8-2", [ 7, 8, 2 ], 462, 44,
|
||
|
|
"issteinerloop", "X793600C9801F4F62" ],
|
||
|
|
[ "Steiner loop", "7.8-2", [ 7, 8, 2 ], 462, 44, "steiner loop",
|
||
|
|
"X793600C9801F4F62" ],
|
||
|
|
[ "loop Steiner", "7.8-2", [ 7, 8, 2 ], 462, 44, "loop steiner",
|
||
|
|
"X793600C9801F4F62" ],
|
||
|
|
[ "\033[2XIsLeftBruckLoop\033[102X", "7.8-3", [ 7, 8, 3 ], 470, 44,
|
||
|
|
"isleftbruckloop", "X85F1BD4280E44F5B" ],
|
||
|
|
[ "\033[2XIsLeftKLoop\033[102X", "7.8-3", [ 7, 8, 3 ], 470, 44,
|
||
|
|
"isleftkloop", "X85F1BD4280E44F5B" ],
|
||
|
|
[ "Bruck loop left", "7.8-3", [ 7, 8, 3 ], 470, 44, "bruck loop left",
|
||
|
|
"X85F1BD4280E44F5B" ],
|
||
|
|
[ "loop left Bruck", "7.8-3", [ 7, 8, 3 ], 470, 44, "loop left bruck",
|
||
|
|
"X85F1BD4280E44F5B" ],
|
||
|
|
[ "K loop left", "7.8-3", [ 7, 8, 3 ], 470, 44, "k loop left",
|
||
|
|
"X85F1BD4280E44F5B" ],
|
||
|
|
[ "loop left K", "7.8-3", [ 7, 8, 3 ], 470, 44, "loop left k",
|
||
|
|
"X85F1BD4280E44F5B" ],
|
||
|
|
[ "\033[2XIsRightBruckLoop\033[102X", "7.8-4", [ 7, 8, 4 ], 480, 44,
|
||
|
|
"isrightbruckloop", "X857B373E7B4E0519" ],
|
||
|
|
[ "\033[2XIsRightKLoop\033[102X", "7.8-4", [ 7, 8, 4 ], 480, 44,
|
||
|
|
"isrightkloop", "X857B373E7B4E0519" ],
|
||
|
|
[ "Bruck loop right", "7.8-4", [ 7, 8, 4 ], 480, 44, "bruck loop right",
|
||
|
|
"X857B373E7B4E0519" ],
|
||
|
|
[ "loop right Bruck", "7.8-4", [ 7, 8, 4 ], 480, 44, "loop right bruck",
|
||
|
|
"X857B373E7B4E0519" ],
|
||
|
|
[ "K loop right", "7.8-4", [ 7, 8, 4 ], 480, 44, "k loop right",
|
||
|
|
"X857B373E7B4E0519" ],
|
||
|
|
[ "loop right K", "7.8-4", [ 7, 8, 4 ], 480, 44, "loop right k",
|
||
|
|
"X857B373E7B4E0519" ],
|
||
|
|
[ "\033[2XAssociatedLeftBruckLoop\033[102X", "8.1-1", [ 8, 1, 1 ], 10, 45,
|
||
|
|
"associatedleftbruckloop", "X8664CA927DD73DBE" ],
|
||
|
|
[ "\033[2XAssociatedRightBruckLoop\033[102X", "8.1-1", [ 8, 1, 1 ], 10, 45,
|
||
|
|
"associatedrightbruckloop", "X8664CA927DD73DBE" ],
|
||
|
|
[ "loop left Bol", "8.1-1", [ 8, 1, 1 ], 10, 45, "loop left bol",
|
||
|
|
"X8664CA927DD73DBE" ],
|
||
|
|
[ "Bol loop left", "8.1-1", [ 8, 1, 1 ], 10, 45, "bol loop left",
|
||
|
|
"X8664CA927DD73DBE" ],
|
||
|
|
[ "Bruck loop associated left", "8.1-1", [ 8, 1, 1 ], 10, 45,
|
||
|
|
"bruck loop associated left", "X8664CA927DD73DBE" ],
|
||
|
|
[ "loop associated left Bruck", "8.1-1", [ 8, 1, 1 ], 10, 45,
|
||
|
|
"loop associated left bruck", "X8664CA927DD73DBE" ],
|
||
|
|
[ "\033[2XIsExactGroupFactorization\033[102X", "8.1-2", [ 8, 1, 2 ], 26,
|
||
|
|
45, "isexactgroupfactorization", "X82FC16F386CE11F1" ],
|
||
|
|
[ "exact group factorization", "8.1-2", [ 8, 1, 2 ], 26, 45,
|
||
|
|
"exact group factorization", "X82FC16F386CE11F1" ],
|
||
|
|
[ "\033[2XRightBolLoopByExactGroupFactorization\033[102X", "8.1-3",
|
||
|
|
[ 8, 1, 3 ], 35, 45, "rightbolloopbyexactgroupfactorization",
|
||
|
|
"X7DCA64807F899127" ],
|
||
|
|
[ "modification Moufang", "8.2", [ 8, 2, 0 ], 47, 46,
|
||
|
|
"modification moufang", "X819F82737C2A860D" ],
|
||
|
|
[ "\033[2XLoopByCyclicModification\033[102X", "8.2-1", [ 8, 2, 1 ], 57, 46,
|
||
|
|
"loopbycyclicmodification", "X7B3165C083709831" ],
|
||
|
|
[ "modification cyclic", "8.2-1", [ 8, 2, 1 ], 57, 46,
|
||
|
|
"modification cyclic", "X7B3165C083709831" ],
|
||
|
|
[ "\033[2XLoopByDihedralModification\033[102X", "8.2-2", [ 8, 2, 2 ], 70,
|
||
|
|
46, "loopbydihedralmodification", "X7D7717C587BC2D1E" ],
|
||
|
|
[ "modification dihedral", "8.2-2", [ 8, 2, 2 ], 70, 46,
|
||
|
|
"modification dihedral", "X7D7717C587BC2D1E" ],
|
||
|
|
[ "\033[2XLoopMG2\033[102X", "8.2-3", [ 8, 2, 3 ], 86, 46, "loopmg2",
|
||
|
|
"X7CC6CDB786E9BBA0" ],
|
||
|
|
[ "Chein loop", "8.2-3", [ 8, 2, 3 ], 86, 46, "chein loop",
|
||
|
|
"X7CC6CDB786E9BBA0" ],
|
||
|
|
[ "loop Chein", "8.2-3", [ 8, 2, 3 ], 86, 46, "loop chein",
|
||
|
|
"X7CC6CDB786E9BBA0" ],
|
||
|
|
[ "group with triality", "8.3", [ 8, 3, 0 ], 98, 46, "group with triality",
|
||
|
|
"X83E73A767D79FAFD" ],
|
||
|
|
[ "\033[2XTrialityPermGroup\033[102X", "8.3-1", [ 8, 3, 1 ], 113, 47,
|
||
|
|
"trialitypermgroup", "X7DB4DE647F6F56F0" ],
|
||
|
|
[ "\033[2XTrialityPcGroup\033[102X", "8.3-2", [ 8, 3, 2 ], 120, 47,
|
||
|
|
"trialitypcgroup", "X82CC977085DFDFE8" ],
|
||
|
|
[ "\033[2XAllLoopTablesInGroup\033[102X", "8.4-1", [ 8, 4, 1 ], 146, 47,
|
||
|
|
"alllooptablesingroup", "X804F40087DD1225D" ],
|
||
|
|
[ "\033[2XAllProperLoopTablesInGroup\033[102X", "8.4-2", [ 8, 4, 2 ], 152,
|
||
|
|
47, "allproperlooptablesingroup", "X7854C8E382DC8E8B" ],
|
||
|
|
[ "\033[2XOneLoopTableInGroup\033[102X", "8.4-3", [ 8, 4, 3 ], 158, 47,
|
||
|
|
"onelooptableingroup", "X7BFFC66A824BA6AA" ],
|
||
|
|
[ "\033[2XOneProperLoopTableInGroup\033[102X", "8.4-4", [ 8, 4, 4 ], 164,
|
||
|
|
48, "oneproperlooptableingroup", "X84C5A76585B335FF" ],
|
||
|
|
[ "\033[2XAllLoopsWithMltGroup\033[102X", "8.4-5", [ 8, 4, 5 ], 170, 48,
|
||
|
|
"allloopswithmltgroup", "X7E5F1C2879358EEF" ],
|
||
|
|
[ "\033[2XOneLoopWithMltGroup\033[102X", "8.4-6", [ 8, 4, 6 ], 176, 48,
|
||
|
|
"oneloopwithmltgroup", "X8266DE05824226E6" ],
|
||
|
|
[ "\033[2XLibraryLoop\033[102X", "9.1-1", [ 9, 1, 1 ], 31, 49,
|
||
|
|
"libraryloop", "X849865D6786EEF9B" ],
|
||
|
|
[ "\033[2XMyLibraryLoop\033[102X", "9.1-2", [ 9, 1, 2 ], 36, 49,
|
||
|
|
"mylibraryloop", "X78C4B8757902D49F" ],
|
||
|
|
[ "\033[2XDisplayLibraryInfo\033[102X", "9.1-3", [ 9, 1, 3 ], 46, 50,
|
||
|
|
"displaylibraryinfo", "X7A64372E81E713B4" ],
|
||
|
|
[ "\033[2XLeftBolLoop\033[102X", "9.2-1", [ 9, 2, 1 ], 67, 50,
|
||
|
|
"leftbolloop", "X7EE99F647C537994" ],
|
||
|
|
[ "\033[2XRightBolLoop\033[102X", "9.2-2", [ 9, 2, 2 ], 72, 50,
|
||
|
|
"rightbolloop", "X8774304282654C58" ],
|
||
|
|
[ "\033[2XMoufangLoop\033[102X", "9.3-1", [ 9, 3, 1 ], 86, 50,
|
||
|
|
"moufangloop", "X81E82098822543EE" ],
|
||
|
|
[ "octonion loop", "9.3-1", [ 9, 3, 1 ], 86, 50, "octonion loop",
|
||
|
|
"X81E82098822543EE" ],
|
||
|
|
[ "loop octonion", "9.3-1", [ 9, 3, 1 ], 86, 50, "loop octonion",
|
||
|
|
"X81E82098822543EE" ],
|
||
|
|
[ "\033[2XCodeLoop\033[102X", "9.4-1", [ 9, 4, 1 ], 117, 51, "codeloop",
|
||
|
|
"X7DB4D3B27BB4D7EE" ],
|
||
|
|
[ "\033[2XSteinerLoop\033[102X", "9.5-1", [ 9, 5, 1 ], 144, 51,
|
||
|
|
"steinerloop", "X87C235457E859AF4" ],
|
||
|
|
[ "\033[2XRCCLoop\033[102X", "9.6-1", [ 9, 6, 1 ], 173, 52, "rccloop",
|
||
|
|
"X806B2DE67990E42F" ],
|
||
|
|
[ "\033[2XRightConjugacyClosedLoop\033[102X", "9.6-1", [ 9, 6, 1 ], 173,
|
||
|
|
52, "rightconjugacyclosedloop", "X806B2DE67990E42F" ],
|
||
|
|
[ "\033[2XLCCLoop\033[102X", "9.6-2", [ 9, 6, 2 ], 180, 52, "lccloop",
|
||
|
|
"X80AB8B107D55FB19" ],
|
||
|
|
[ "\033[2XLeftConjugacyClosedLoop\033[102X", "9.6-2", [ 9, 6, 2 ], 180, 52,
|
||
|
|
"leftconjugacyclosedloop", "X80AB8B107D55FB19" ],
|
||
|
|
[ "\033[2XCCLoop\033[102X", "9.6-3", [ 9, 6, 3 ], 217, 52, "ccloop",
|
||
|
|
"X798BC601843E8916" ],
|
||
|
|
[ "\033[2XConjugacyClosedLoop\033[102X", "9.6-3", [ 9, 6, 3 ], 217, 52,
|
||
|
|
"conjugacyclosedloop", "X798BC601843E8916" ],
|
||
|
|
[ "\033[2XSmallLoop\033[102X", "9.7-1", [ 9, 7, 1 ], 230, 53, "smallloop",
|
||
|
|
"X7C6EE23E84CD87D3" ],
|
||
|
|
[ "Paige loop", "9.8", [ 9, 8, 0 ], 235, 53, "paige loop",
|
||
|
|
"X8135C8FD8714C606" ],
|
||
|
|
[ "loop Paige", "9.8", [ 9, 8, 0 ], 235, 53, "loop paige",
|
||
|
|
"X8135C8FD8714C606" ],
|
||
|
|
[ "\033[2XPaigeLoop\033[102X", "9.8-1", [ 9, 8, 1 ], 244, 53, "paigeloop",
|
||
|
|
"X7FCF4D6B7AD66D74" ],
|
||
|
|
[ "\033[2XNilpotentLoop\033[102X", "9.9-1", [ 9, 9, 1 ], 261, 53,
|
||
|
|
"nilpotentloop", "X7A9C960D86E2AD28" ],
|
||
|
|
[ "\033[2XAutomorphicLoop\033[102X", "9.10-1", [ 9, 10, 1 ], 278, 53,
|
||
|
|
"automorphicloop", "X784FFA9E7FDA9F43" ],
|
||
|
|
[ "sedenion loop", "9.11", [ 9, 11, 0 ], 283, 54, "sedenion loop",
|
||
|
|
"X843BD73F788049F7" ],
|
||
|
|
[ "loop sedenion", "9.11", [ 9, 11, 0 ], 283, 54, "loop sedenion",
|
||
|
|
"X843BD73F788049F7" ],
|
||
|
|
[ "\033[2XInterestingLoop\033[102X", "9.11-1", [ 9, 11, 1 ], 293, 54,
|
||
|
|
"interestingloop", "X87F24AD3811910D3" ],
|
||
|
|
[ "\033[2XItpSmallLoop\033[102X", "9.12-1", [ 9, 12, 1 ], 306, 54,
|
||
|
|
"itpsmallloop", "X850C4C01817A098D" ] ]
|
||
|
|
);
|