73 lines
3.1 KiB
Plaintext
73 lines
3.1 KiB
Plaintext
#############################################################################
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##
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#W automorphic.tbl Automorphic loops G. P. Nagy / P. Vojtechovsky
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##
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#H @(#)$Id: automorphic.tbl, v 3.4.0 2017/10/23 gap Exp $
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##
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#Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary),
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#Y P. Vojtechovsky (University of Denver, USA)
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##
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LOOPS_automorphic_data := [
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#implemented orders
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[3,6,8,9,10,12,14,15,27,81],
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#number of nonassociative loops of given order
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[1,1,7,2,3,2,5,2,7,72],
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#the loops
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[
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#order 3 (Z_3, use left Bruck loops, placeholder only)
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[
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],
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#order 6
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[
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"2045301534540123520143120"
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],
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#order 8
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[
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"0325476301674521076545670132476102374532016542310",
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"0325476301674521076545670312476302174512036542130",
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"0325476301674521076545671023476013274523106543201",
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"0325476301675421076455671023476013275423106453201",
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"0325476301675421076455760123467103274532106542301",
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"0325476301675421076455760132467102374523106543201",
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"0325476310674520176545761023467013275432106452301"
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],
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#order 9 (two abelian groups, use left Bruck loops, placeholder only)
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[
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]
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,
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#order 10
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[
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"234067895340178956401289567012395678987601234598740123659834012765923401876512340",
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"234067895340178956401289567012395678987603142598720314659842031765914203876531420",
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"234067895340178956401289567012395678987602413598730241659813024765941302876524130"
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],
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#order 12
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[
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"23450789AB63450189AB67450129AB67850123AB678901234B6789ABA9870123456BA9850123476BA9450123876BA3450129876B234501A9876123450",
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"23450789AB63450189AB67450129AB67850123AB678901234B6789ABA9873450126BA9823450176BA9123450876BA0123459876B501234A9876450123"
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],
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#order 14
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[
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"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9801234567DCBA9601234587DCBA5601234987DCB4560123A987DC3456012BA987D2345601CBA9871234560",
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"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9804152637DCBA9304152687DCBA6304152987DCB2630415A987DC5263041BA987D1526304CBA9874152630",
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"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9805316427DCBA9205316487DCBA4205316987DCB6420531A987DC1642053BA987D3164205CBA9875316420",
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"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9802461357DCBA9502461387DCBA3502461987DCB1350246A987DC6135024BA987D4613502CBA9872461350",
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"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9803625147DCBA9403625187DCBA1403625987DCB5140362A987DC2514036BA987D6251403CBA9873625140"
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],
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#order 15
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[
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"234068597BDAEC340189675DEBCA401297856ECDAB012375968CAEBD6897ADECB041328975DCABE430215689EABDC102439756CBDEA324107568BECAD21304BDEC0413258976DECA4302187569ABDE1024395687ECAB3241076895CABD2130469758",
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"234067895BCDEA340178956CDEAB401289567DEABC012395678EABCD7968ADBEC012348579ECADB340129685DBECA123405796CADBE401236857BECAD23401DBEC0432156789ECAD3210478956ADBE1043295678BECA4321067895CADB2104389567"
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],
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#order 27 (commutative only, use left Bruck loops, placeholder)
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[
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]
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,
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#order 81 (commutative only, use left Bruck loops, placeholder)
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[
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]
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]
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];
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