486 lines
19 KiB
Plaintext
486 lines
19 KiB
Plaintext
\begin{theindex}
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\item \texttt {AllLoopsWithMltGroup}, \hyperpage{48}
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\item \texttt {AllLoopTablesInGroup}, \hyperpage{47}
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\item \texttt {AllProperLoopTablesInGroup}, \hyperpage{47}
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\item \texttt {AllSubloops}, \hyperpage{28}
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\item \texttt {AllSubquasigroups}, \hyperpage{27}
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\item alternative loop, \hyperpage{39}
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\subitem left, \hyperpage{39}
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\subitem right, \hyperpage{39}
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\item antiautomorphic inverse property, \hyperpage{37}
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\item \texttt {AreEqualDiscriminators}, \hyperpage{35}
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\item \texttt {AssociatedLeftBruckLoop}, \hyperpage{45}
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\item \texttt {AssociatedRightBruckLoop}, \hyperpage{45}
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\item \texttt {Associator}, \hyperpage{24}
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\item associator, \hyperpage{9}
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\item associator subloop, \hyperpage{9}
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\item \texttt {AssociatorSubloop}, \hyperpage{31}
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\item automorphic inverse property, \hyperpage{37}
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\item automorphic loop, \hyperpage{43}
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\subitem left, \hyperpage{43}
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\subitem middle, \hyperpage{43}
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\subitem right, \hyperpage{43}
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\item \texttt {AutomorphicLoop}, \hyperpage{53}
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\item \texttt {AutomorphismGroup}, \hyperpage{34}
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\indexspace
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\item Bol loop
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\subitem left, \hyperpage{12}, \hyperpage{39}, \hyperpage{45}
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\subitem right, \hyperpage{39}
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\item Bruck loop
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\subitem associated left, \hyperpage{45}
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\subitem left, \hyperpage{44}
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\subitem right, \hyperpage{44}
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\indexspace
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\item C loop, \hyperpage{39}
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\item \texttt {CanonicalCayleyTable}, \hyperpage{15}
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\item \texttt {CanonicalCopy}, \hyperpage{15}
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\item Cayley table, \hyperpage{14}
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\subitem canonical, \hyperpage{15}
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\item \texttt {CayleyTable}, \hyperpage{22}
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\item \texttt {CayleyTableByPerms}, \hyperpage{17}
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\item \texttt {CCLoop}, \hyperpage{52}
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\item \texttt {Center}, \hyperpage{31}
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\item center, \hyperpage{9}
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\item central series
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\subitem lower, \hyperpage{33}
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\subitem upper, \hyperpage{9}
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\item Chein loop, \hyperpage{46}
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\item cocycle, \hyperpage{18}
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\item code loop, \hyperpage{44}
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\item \texttt {CodeLoop}, \hyperpage{51}
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\item \texttt {Commutant}, \hyperpage{31}
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\item commutant, \hyperpage{9}
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\item \texttt {Commutator}, \hyperpage{24}
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\item commutator, \hyperpage{9}
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\item conjugacy closed loop, \hyperpage{42}
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\subitem left, \hyperpage{42}
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\subitem right, \hyperpage{42}
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\item \texttt {ConjugacyClosedLoop}, \hyperpage{52}
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\item conjugation, \hyperpage{30}
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\item coset, \hyperpage{28}
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\indexspace
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\item derived series, \hyperpage{9}
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\item derived subloop, \hyperpage{9}
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\item \texttt {DerivedLength}, \hyperpage{33}
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\item \texttt {DerivedSubloop}, \hyperpage{33}
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\item diassociative quasigroup, \hyperpage{37}
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\item \texttt {DirectProduct}, \hyperpage{21}
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\item \texttt {Discriminator}, \hyperpage{35}
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\item \texttt {DisplayLibraryInfo}, \hyperpage{50}
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\item distributive quasigroup, \hyperpage{38}
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\subitem left, \hyperpage{38}
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\subitem right, \hyperpage{38}
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\item division
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\subitem left, \hyperpage{8}
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\subitem right, \hyperpage{8}
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\indexspace
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\item \texttt {Elements}, \hyperpage{22}
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\item entropic quasigroup, \hyperpage{39}
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\item exact group factorization, \hyperpage{45}
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\item \texttt {Exponent}, \hyperpage{23}
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\item exponent, \hyperpage{23}
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\item extension, \hyperpage{18}
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\subitem nuclear, \hyperpage{18}
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\item extra loop, \hyperpage{39}
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\indexspace
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\item \texttt {FactorLoop}, \hyperpage{32}
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\item flexible loop, \hyperpage{39}
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\item folder
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\subitem quasigroup, \hyperpage{18}
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\item Frattini subloop, \hyperpage{33}
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\item \texttt {FrattinifactorSize}, \hyperpage{33}
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\item \texttt {FrattiniSubloop}, \hyperpage{33}
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\indexspace
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\item \texttt {GeneratorsOfLoop}, \hyperpage{24}
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\item \texttt {GeneratorsOfQuasigroup}, \hyperpage{24}
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\item \texttt {GeneratorsSmallest}, \hyperpage{25}
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\item group, \hyperpage{8}
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\item group with triality, \hyperpage{46}
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\item groupoid, \hyperpage{8}
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\indexspace
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\item \texttt {HasAntiautomorphicInverseProperty}, \hyperpage{37}
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\item \texttt {HasAutomorphicInverseProperty}, \hyperpage{37}
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\item \texttt {HasInverseProperty}, \hyperpage{37}
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\item \texttt {HasLeftInverseProperty}, \hyperpage{37}
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\item \texttt {HasRightInverseProperty}, \hyperpage{37}
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\item \texttt {HasTwosidedInverses}, \hyperpage{37}
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\item \texttt {HasWeakInverseProperty}, \hyperpage{37}
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\item homomorphism, \hyperpage{9}
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\item homotopism, \hyperpage{10}
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\indexspace
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\item idempotent quasigroup, \hyperpage{38}
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\item identity
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\subitem element, \hyperpage{8}
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\subitem of Bol-Moufang type, \hyperpage{39}
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\item inner mapping
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\subitem left, \hyperpage{29}
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\subitem middle, \hyperpage{30}
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\subitem right, \hyperpage{29}
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\item inner mapping group, \hyperpage{9}
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\subitem left, \hyperpage{9}
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\subitem middle, \hyperpage{30}
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\subitem right, \hyperpage{9}
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\item \texttt {InnerMappingGroup}, \hyperpage{30}
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\item \texttt {InterestingLoop}, \hyperpage{54}
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\item \texttt {IntoGroup}, \hyperpage{20}
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\item \texttt {IntoLoop}, \hyperpage{20}
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\item \texttt {IntoQuasigroup}, \hyperpage{20}
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\item \texttt {Inverse}, \hyperpage{24}
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\item inverse, \hyperpage{24}
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\subitem left, \hyperpage{24}, \hyperpage{37}
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\subitem right, \hyperpage{24}, \hyperpage{37}
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\subitem two-sided, \hyperpage{8}, \hyperpage{37}
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\item inverse property, \hyperpage{37}
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\subitem antiautomorphic, \hyperpage{37}
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\subitem automorphic, \hyperpage{37}
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\subitem left, \hyperpage{37}
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\subitem right, \hyperpage{37}
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\subitem weak, \hyperpage{37}
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\item \texttt {IsALoop}, \hyperpage{44}
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\item \texttt {IsAlternative}, \hyperpage{41}
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\item \texttt {IsAssociative}, \hyperpage{36}
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\item \texttt {IsAutomorphicLoop}, \hyperpage{44}
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\item \texttt {IsCCLoop}, \hyperpage{42}
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\item \texttt {IsCLoop}, \hyperpage{40}
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\item \texttt {IsCodeLoop}, \hyperpage{44}
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\item \texttt {IsCommutative}, \hyperpage{36}
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\item \texttt {IsConjugacyClosedLoop}, \hyperpage{42}
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\item \texttt {IsDiassociative}, \hyperpage{36}
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\item \texttt {IsDistributive}, \hyperpage{38}
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\item \texttt {IsEntropic}, \hyperpage{39}
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\item \texttt {IsExactGroupFactorization}, \hyperpage{45}
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\item \texttt {IsExtraLoop}, \hyperpage{40}
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\item \texttt {IsFlexible}, \hyperpage{41}
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\item \texttt {IsIdempotent}, \hyperpage{38}
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\item \texttt {IsLCCLoop}, \hyperpage{42}
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\item \texttt {IsLCLoop}, \hyperpage{40}
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\item \texttt {IsLeftALoop}, \hyperpage{43}
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\item \texttt {IsLeftAlternative}, \hyperpage{41}
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\item \texttt {IsLeftAutomorphicLoop}, \hyperpage{43}
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\item \texttt {IsLeftBolLoop}, \hyperpage{40}
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\item \texttt {IsLeftBruckLoop}, \hyperpage{44}
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\item \texttt {IsLeftConjugacyClosedLoop}, \hyperpage{42}
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\item \texttt {IsLeftDistributive}, \hyperpage{38}
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\item \texttt {IsLeftKLoop}, \hyperpage{44}
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\item \texttt {IsLeftNuclearSquareLoop}, \hyperpage{40}
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\item \texttt {IsLeftPowerAlternative}, \hyperpage{42}
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\item IsLoop, \hyperpage{11}
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\item \texttt {IsLoopCayleyTable}, \hyperpage{14}
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\item IsLoopElement, \hyperpage{11}
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\item \texttt {IsLoopTable}, \hyperpage{14}
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\item \texttt {IsMedial}, \hyperpage{39}
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\item \texttt {IsMiddleALoop}, \hyperpage{43}
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\item \texttt {IsMiddleAutomorphicLoop}, \hyperpage{43}
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\item \texttt {IsMiddleNuclearSquareLoop}, \hyperpage{40}
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\item \texttt {IsMoufangLoop}, \hyperpage{40}
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\item \texttt {IsNilpotent}, \hyperpage{32}
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\item \texttt {IsNormal}, \hyperpage{31}
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\item \texttt {IsNuclearSquareLoop}, \hyperpage{41}
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\item \texttt {IsomorphicCopyByNormalSubloop}, \hyperpage{34}
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\item \texttt {IsomorphicCopyByPerm}, \hyperpage{34}
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\item isomorphism, \hyperpage{9}
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\item \texttt {IsomorphismLoops}, \hyperpage{34}
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\item \texttt {IsomorphismQuasigroups}, \hyperpage{33}
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\item \texttt {IsOsbornLoop}, \hyperpage{42}
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\item isotopism, \hyperpage{10}
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\subitem principal, \hyperpage{10}
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\item \texttt {IsotopismLoops}, \hyperpage{35}
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\item \texttt {IsPowerAlternative}, \hyperpage{42}
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\item \texttt {IsPowerAssociative}, \hyperpage{36}
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\item IsQuasigroup, \hyperpage{11}
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\item \texttt {IsQuasigroupCayleyTable}, \hyperpage{14}
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\item IsQuasigroupElement, \hyperpage{11}
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\item \texttt {IsQuasigroupTable}, \hyperpage{14}
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\item \texttt {IsRCCLoop}, \hyperpage{42}
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\item \texttt {IsRCLoop}, \hyperpage{40}
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\item \texttt {IsRightALoop}, \hyperpage{44}
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\item \texttt {IsRightAlternative}, \hyperpage{41}
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\item \texttt {IsRightAutomorphicLoop}, \hyperpage{44}
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\item \texttt {IsRightBolLoop}, \hyperpage{40}
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\item \texttt {IsRightBruckLoop}, \hyperpage{44}
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\item \texttt {IsRightConjugacyClosedLoop}, \hyperpage{42}
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\item \texttt {IsRightDistributive}, \hyperpage{38}
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\item \texttt {IsRightKLoop}, \hyperpage{44}
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\item \texttt {IsRightNuclearSquareLoop}, \hyperpage{40}
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\item \texttt {IsRightPowerAlternative}, \hyperpage{42}
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\item \texttt {IsSemisymmetric}, \hyperpage{38}
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\item \texttt {IsSimple}, \hyperpage{32}
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\item \texttt {IsSolvable}, \hyperpage{33}
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\item \texttt {IsSteinerLoop}, \hyperpage{44}
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\item \texttt {IsSteinerQuasigroup}, \hyperpage{38}
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\item \texttt {IsStronglyNilpotent}, \hyperpage{32}
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\item \texttt {IsSubloop}, \hyperpage{27}
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\item \texttt {IsSubquasigroup}, \hyperpage{27}
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\item \texttt {IsTotallySymmetric}, \hyperpage{38}
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\item \texttt {IsUnipotent}, \hyperpage{38}
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\item \texttt {ItpSmallLoop}, \hyperpage{54}
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\indexspace
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\item K loop
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\subitem left, \hyperpage{44}
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\subitem right, \hyperpage{44}
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\indexspace
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\item latin square, \hyperpage{8}, \hyperpage{14}
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\subitem random, \hyperpage{19}
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\item LC loop, \hyperpage{39}
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\item \texttt {LCCLoop}, \hyperpage{52}
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\item \texttt {LeftBolLoop}, \hyperpage{50}
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\item \texttt {LeftConjugacyClosedLoop}, \hyperpage{52}
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\item \texttt {LeftDivision}, \hyperpage{23}
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\item \texttt {LeftDivisionCayleyTable}, \hyperpage{23}
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\item \texttt {LeftInnerMapping}, \hyperpage{30}
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\item \texttt {LeftInnerMappingGroup}, \hyperpage{30}
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\item \texttt {LeftInverse}, \hyperpage{24}
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\item \texttt {LeftMultiplicationGroup}, \hyperpage{29}
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\item \texttt {LeftNucleus}, \hyperpage{30}
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\item \texttt {LeftSection}, \hyperpage{28}
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\item \texttt {LeftTranslation}, \hyperpage{28}
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\item \texttt {LibraryLoop}, \hyperpage{49}
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\item loop, \hyperpage{8}
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\subitem alternative, \hyperpage{39}
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\subitem associated left Bruck, \hyperpage{45}
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\subitem automorphic, \hyperpage{43}
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\subitem C, \hyperpage{39}
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\subitem Chein, \hyperpage{46}
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\subitem code, \hyperpage{44}
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\subitem conjugacy closed, \hyperpage{42}
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\subitem extra, \hyperpage{39}
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\subitem flexible, \hyperpage{39}
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\subitem LC, \hyperpage{39}
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\subitem left alternative, \hyperpage{39}
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\subitem left automorphic, \hyperpage{43}
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\subitem left Bol, \hyperpage{12}, \hyperpage{39}, \hyperpage{45}
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\subitem left Bruck, \hyperpage{44}
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\subitem left conjugacy closed, \hyperpage{42}
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\subitem left K, \hyperpage{44}
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\subitem left nuclear square, \hyperpage{39}
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\subitem left power alternative, \hyperpage{42}
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\subitem middle automorphic, \hyperpage{43}
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\subitem middle nuclear square, \hyperpage{39}
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\subitem Moufang, \hyperpage{39}
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\subitem nilpotent, \hyperpage{9}, \hyperpage{19}
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\subitem nuclear square, \hyperpage{39}
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\subitem octonion, \hyperpage{50}
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\subitem of Bol-Moufang type, \hyperpage{39}
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\subitem Osborn, \hyperpage{43}
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\subitem Paige, \hyperpage{53}
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\subitem power alternative, \hyperpage{42}
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\subitem power associative, \hyperpage{23}
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\subitem RC, \hyperpage{39}
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\subitem right alternative, \hyperpage{39}
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\subitem right automorphic, \hyperpage{43}
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\subitem right Bol, \hyperpage{39}
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\subitem right Bruck, \hyperpage{44}
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\subitem right conjugacy closed, \hyperpage{42}
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\subitem right K, \hyperpage{44}
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\subitem right nuclear square, \hyperpage{39}
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\subitem right power alternative, \hyperpage{42}
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\subitem sedenion, \hyperpage{54}
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\subitem simple, \hyperpage{12}, \hyperpage{32}
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\subitem solvable, \hyperpage{9}
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\subitem Steiner, \hyperpage{44}
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\subitem strongly nilpotent, \hyperpage{32}
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\item loop isotope
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\subitem principal, \hyperpage{10}
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\item loop table, \hyperpage{14}
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\item \texttt {LoopByCayleyTable}, \hyperpage{15}
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\item \texttt {LoopByCyclicModification}, \hyperpage{46}
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\item \texttt {LoopByDihedralModification}, \hyperpage{46}
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\item \texttt {LoopByExtension}, \hyperpage{18}
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\item \texttt {LoopByLeftSection}, \hyperpage{17}
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\item \texttt {LoopByRightFolder}, \hyperpage{18}
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\item \texttt {LoopByRightSection}, \hyperpage{17}
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\item \texttt {LoopFromFile}, \hyperpage{17}
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\item \texttt {LoopMG2}, \hyperpage{46}
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\item \texttt {LoopsUpToIsomorphism}, \hyperpage{34}
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\item \texttt {LoopsUpToIsotopism}, \hyperpage{35}
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\item \texttt {LowerCentralSeries}, \hyperpage{33}
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\indexspace
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\item magma, \hyperpage{8}
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\item medial quasigroup, \hyperpage{39}
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\item \texttt {MiddleInnerMapping}, \hyperpage{30}
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\item \texttt {MiddleInnerMappingGroup}, \hyperpage{30}
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\item \texttt {MiddleNucleus}, \hyperpage{30}
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\item modification
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\subitem cyclic, \hyperpage{46}
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\subitem dihedral, \hyperpage{46}
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\subitem Moufang, \hyperpage{46}
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\item Moufang loop, \hyperpage{39}
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\item \texttt {MoufangLoop}, \hyperpage{50}
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\item multiplication group, \hyperpage{9}
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\subitem left, \hyperpage{9}
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\subitem relative, \hyperpage{29}
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\subitem relative left, \hyperpage{29}
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\subitem relative right , \hyperpage{29}
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\subitem right, \hyperpage{9}
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\item multiplication table, \hyperpage{14}
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\item \texttt {MultiplicationGroup}, \hyperpage{29}
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\item \texttt {MyLibraryLoop}, \hyperpage{49}
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\indexspace
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\item \texttt {NaturalHomomorphismByNormalSubloop}, \hyperpage{32}
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\item neutral element, \hyperpage{8}
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\item nilpotence class, \hyperpage{9}
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\item \texttt {NilpotencyClassOfLoop}, \hyperpage{32}
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\item nilpotent loop, \hyperpage{9}
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\subitem strongly, \hyperpage{32}
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\item \texttt {NilpotentLoop}, \hyperpage{53}
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\item normal closure, \hyperpage{31}
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\item normal subloop, \hyperpage{31}
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\item \texttt {NormalClosure}, \hyperpage{31}
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\item \texttt {NormalizedQuasigroupTable}, \hyperpage{15}
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\item \texttt {Nuc}, \hyperpage{31}
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\item nuclear square loop, \hyperpage{39}
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\subitem left, \hyperpage{39}
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\subitem middle, \hyperpage{39}
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\subitem right, \hyperpage{39}
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\item \texttt {NuclearExtension}, \hyperpage{18}
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\item nucleus, \hyperpage{9}
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\subitem left, \hyperpage{9}
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\subitem middle, \hyperpage{9}
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\subitem right, \hyperpage{9}
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\item \texttt {NucleusOfLoop}, \hyperpage{31}
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\item \texttt {NucleusOfQuasigroup}, \hyperpage{31}
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\indexspace
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\item octonion loop, \hyperpage{50}
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\item \texttt {One}, \hyperpage{22}
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\item \texttt {OneLoopTableInGroup}, \hyperpage{47}
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\item \texttt {OneLoopWithMltGroup}, \hyperpage{48}
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\item \texttt {OneProperLoopTableInGroup}, \hyperpage{48}
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\item \texttt {Opposite}, \hyperpage{21}
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\item opposite quasigroup, \hyperpage{21}
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\item \texttt {OppositeLoop}, \hyperpage{21}
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\item \texttt {OppositeQuasigroup}, \hyperpage{21}
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\item Osborn loop, \hyperpage{43}
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\indexspace
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\item Paige loop, \hyperpage{53}
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\item \texttt {PaigeLoop}, \hyperpage{53}
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\item \texttt {Parent}, \hyperpage{26}
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\item \texttt {PosInParent}, \hyperpage{27}
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\item \texttt {Position}, \hyperpage{26}
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\item power alternative loop, \hyperpage{42}
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\subitem left, \hyperpage{42}
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\subitem right, \hyperpage{42}
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\item power associative loop, \hyperpage{23}
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\item power associative quasigroup, \hyperpage{36}
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\item \texttt {PrincipalLoopIsotope}, \hyperpage{20}
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\indexspace
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\item quasigroup, \hyperpage{8}
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\subitem diassociative, \hyperpage{37}
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\subitem distributive, \hyperpage{38}
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\subitem entropic, \hyperpage{39}
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\subitem idempotent, \hyperpage{38}
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\subitem left distributive, \hyperpage{38}
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\subitem medial, \hyperpage{39}
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\subitem opposite, \hyperpage{21}
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\subitem power associative, \hyperpage{36}
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\subitem right distributive, \hyperpage{38}
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\subitem semisymmetric, \hyperpage{38}
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\subitem Steiner, \hyperpage{38}
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\subitem totally symmetric, \hyperpage{38}
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\subitem unipotent, \hyperpage{38}
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\item quasigroup table, \hyperpage{14}
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\item \texttt {QuasigroupByCayleyTable}, \hyperpage{15}
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\item \texttt {QuasigroupByLeftSection}, \hyperpage{17}
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\item \texttt {QuasigroupByRightFolder}, \hyperpage{18}
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\item \texttt {QuasigroupByRightSection}, \hyperpage{17}
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\item \texttt {QuasigroupFromFile}, \hyperpage{17}
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\item \texttt {QuasigroupsUpToIsomorphism}, \hyperpage{34}
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\indexspace
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\item \texttt {RandomLoop}, \hyperpage{19}
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\item \texttt {RandomNilpotentLoop}, \hyperpage{19}
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\item \texttt {RandomQuasigroup}, \hyperpage{19}
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\item RC loop, \hyperpage{39}
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\item \texttt {RCCLoop}, \hyperpage{52}
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\item \texttt {RelativeLeftMultiplicationGroup}, \hyperpage{29}
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\item \texttt {RelativeMultiplicationGroup}, \hyperpage{29}
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\item \texttt {RelativeRightMultiplicationGroup}, \hyperpage{29}
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\item \texttt {RightBolLoop}, \hyperpage{50}
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\item \texttt {Right}\discretionary {-}{}{}\texttt {Bol}\discretionary {-}{}{}\texttt {Loop}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Exact}\discretionary {-}{}{}\texttt {Group}\discretionary {-}{}{}\texttt {Factorization},
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\hyperpage{45}
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\item \texttt {RightConjugacyClosedLoop}, \hyperpage{52}
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\item \texttt {RightCosets}, \hyperpage{28}
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\item \texttt {RightDivision}, \hyperpage{23}
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\item \texttt {RightDivisionCayleyTable}, \hyperpage{23}
|
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\item \texttt {RightInnerMapping}, \hyperpage{30}
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\item \texttt {RightInnerMappingGroup}, \hyperpage{30}
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\item \texttt {RightInverse}, \hyperpage{24}
|
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\item \texttt {RightMultiplicationGroup}, \hyperpage{29}
|
|
\item \texttt {RightNucleus}, \hyperpage{30}
|
|
\item \texttt {RightSection}, \hyperpage{28}
|
|
\item \texttt {RightTranslation}, \hyperpage{28}
|
|
\item \texttt {RightTransversal}, \hyperpage{28}
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|
|
|
\indexspace
|
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\item section
|
|
\subitem left, \hyperpage{8}
|
|
\subitem right, \hyperpage{8}
|
|
\item sedenion loop, \hyperpage{54}
|
|
\item semisymmetric quasigroup, \hyperpage{38}
|
|
\item \texttt {SetLoopElmName}, \hyperpage{13}
|
|
\item \texttt {SetQuasigroupElmName}, \hyperpage{13}
|
|
\item simple loop, \hyperpage{12}, \hyperpage{32}
|
|
\item \texttt {Size}, \hyperpage{22}
|
|
\item \texttt {SmallGeneratingSet}, \hyperpage{25}
|
|
\item \texttt {SmallLoop}, \hyperpage{53}
|
|
\item solvability class, \hyperpage{9}
|
|
\item solvable loop, \hyperpage{9}
|
|
\item Steiner loop, \hyperpage{44}
|
|
\item Steiner quasigroup, \hyperpage{38}
|
|
\item \texttt {SteinerLoop}, \hyperpage{51}
|
|
\item strongly nilpotent loop, \hyperpage{32}
|
|
\item \texttt {Subloop}, \hyperpage{27}
|
|
\item subloop, \hyperpage{9}
|
|
\subitem normal, \hyperpage{9}, \hyperpage{31}
|
|
\item \texttt {Subquasigroup}, \hyperpage{27}
|
|
\item subquasigroup, \hyperpage{9}
|
|
|
|
\indexspace
|
|
|
|
\item totally symmetric quasigroup, \hyperpage{38}
|
|
\item translation
|
|
\subitem left, \hyperpage{8}
|
|
\subitem right, \hyperpage{8}
|
|
\item transversal, \hyperpage{28}
|
|
\item \texttt {TrialityPcGroup}, \hyperpage{47}
|
|
\item \texttt {TrialityPermGroup}, \hyperpage{47}
|
|
|
|
\indexspace
|
|
|
|
\item unipotent quasigroup, \hyperpage{38}
|
|
\item \texttt {UpperCentralSeries}, \hyperpage{33}
|
|
|
|
\end{theindex}
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