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<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLor </script> <title>GAP (Loops) - Index</title> <meta http-equiv="content-type" content="text/html; charset=UTF-8" /> <meta name="generator" content="GAPDoc2HTML" /> <link rel="stylesheet" type="text/css" href="manual.css" /> <script src="manual.js" type="text/javascript"></script> <script type="text/javascript">overwriteStyle();</script> </head> <body class="chapInd" onload="jscontent()"> <div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top< <div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a> <a href="chap0_mj.ht <p id="mathjaxlink" class="pcenter"><a href="chapInd.html">[MathJax off]</a></p> <p><a id="X83A0356F839C696F" name="X83A0356F839C696F"></a></p> <div class="index"> <h3>Index</h3> <code class="func">AllLoopsWithMltGroup</code> <a href="chap8_mj.html#X7E5F1C2879358EEF"> <code class="func">AllLoopTablesInGroup</code> <a href="chap8_mj.html#X804F40087DD1225D"> <code class="func">AllProperLoopTablesInGroup</code> <a href="chap8_mj.html#X7854C8E382D <code class="func">AllSubloops</code> <a href="chap6_mj.html#X81EF252585592001">6.2-5</a> <br <code class="func">AllSubquasigroups</code> <a href="chap6_mj.html#X859B6C8183537E75">6.2 alternative loop <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> left <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> right <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> antiautomorphic inverse property <a href="chap7_mj.html#X8538D4638232DB51">7.2-5</a> <br /> <code class="func">AreEqualDiscriminators</code> <a href="chap6_mj.html#X812F0DEE7C896E1 <code class="func">AssociatedLeftBruckLoop</code> <a href="chap8_mj.html#X8664CA927DD73D <code class="func">AssociatedRightBruckLoop</code> <a href="chap8_mj.html#X8664CA927DD73 associator <a href="chap2_mj.html#X7E0849977869E53D">2.5</a> <br /> <code class="func">Associator</code> <a href="chap5_mj.html#X82B7448879B91F7B">5.4-1</a> <br /> associator subloop <a href="chap2_mj.html#X7E0849977869E53D">2.5</a> <br /> <code class="func">AssociatorSubloop</code> <a href="chap6_mj.html#X7F7FDE82780EDD7E">6.6 automorphic inverse property <a href="chap7_mj.html#X7F46CE6B7D387158">7.2-4</a> <br /> automorphic loop <a href="chap7_mj.html#X793B22EA8643C667">7.7</a> <br /> left <a href="chap7_mj.html#X793B22EA8643C667">7.7</a> <br /> middle <a href="chap7_mj.html#X793B22EA8643C667">7.7</a> <br /> right <a href="chap7_mj.html#X793B22EA8643C667">7.7</a> <br /> <code class="func">AutomorphicLoop</code> <a href="chap9_mj.html#X784FFA9E7FDA9F43">9.11- <code class="func">AutomorphismGroup</code> <a href="chap6_mj.html#X87677B0787B4461A">6.1 Bol loop, left <a href="chap3_mj.html#X87E49ED884FA6DC4">3.3</a> <a href="chap7_mj.html#X78 right <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> Bruck loop, associated left <a href="chap8_mj.html#X8664CA927DD73DBE">8.1-1</a> <br /> left <a href="chap7_mj.html#X85F1BD4280E44F5B">7.8-3</a> <br /> right <a href="chap7_mj.html#X857B373E7B4E0519">7.8-4</a> <br /> C loop <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> <code class="func">CanonicalCayleyTable</code> <a href="chap4_mj.html#X7971CCB87DAFF7B9"> <code class="func">CanonicalCopy</code> <a href="chap4_mj.html#X7B816D887F46E6B7">4.3-2</a> < Cayley table <a href="chap4_mj.html#X7DE8405B82BC36A9">4.1</a> <br /> canonical <a href="chap4_mj.html#X7971CCB87DAFF7B9">4.3-1</a> <br /> <code class="func">CayleyTable</code> <a href="chap5_mj.html#X85457FA27DE7114D">5.1-2</a> <br <code class="func">CayleyTableByPerms</code> <a href="chap4_mj.html#X7F94C8DD7E1A3470">4. <code class="func">CCLoop</code> <a href="chap9_mj.html#X798BC601843E8916">9.7-3</a> <br /> center <a href="chap2_mj.html#X83EDF04F7952143F">2.3</a> <br /> <code class="func">Center</code> <a href="chap6_mj.html#X7C1FBE7A84DD4873">6.6-4</a> <br /> central series, lower <a href="chap6_mj.html#X817BDBC2812992ED">6.9-5</a> <br /> upper <a href="chap2_mj.html#X869CBCE381E2C422">2.4</a> <br /> Chein loop <a href="chap8_mj.html#X7CC6CDB786E9BBA0">8.2-3</a> <br /> cocycle <a href="chap4_mj.html#X8759431780AC81A9">4.8</a> <br /> code loop <a href="chap7_mj.html#X790FA1188087D5C1">7.8-1</a> <br /> <code class="func">CodeLoop</code> <a href="chap9_mj.html#X7DB4D3B27BB4D7EE">9.5-1</a> <br /> commutant <a href="chap2_mj.html#X83EDF04F7952143F">2.3</a> <br /> <code class="func">Commutant</code> <a href="chap6_mj.html#X7C8428DE791F3CE1">6.6-3</a> <br /> commutator <a href="chap2_mj.html#X7E0849977869E53D">2.5</a> <br /> <code class="func">Commutator</code> <a href="chap5_mj.html#X7D624A9587FB1FE5">5.4-2</a> <br /> conjugacy closed loop <a href="chap7_mj.html#X8176B2C47A4629CD">7.6</a> <br /> left <a href="chap7_mj.html#X8176B2C47A4629CD">7.6</a> <br /> right <a href="chap7_mj.html#X8176B2C47A4629CD">7.6</a> <br /> <code class="func">ConjugacyClosedLoop</code> <a href="chap9_mj.html#X798BC601843E8916">9 conjugation <a href="chap6_mj.html#X8740D61178ACD217">6.5</a> <br /> coset <a href="chap6_mj.html#X835F48248571364F">6.2-6</a> <br /> derived series <a href="chap2_mj.html#X869CBCE381E2C422">2.4</a> <br /> derived subloop <a href="chap2_mj.html#X869CBCE381E2C422">2.4</a> <br /> <code class="func">DerivedLength</code> <a href="chap6_mj.html#X7A9AA1577CEC891F">6.10-3</ <code class="func">DerivedSubloop</code> <a href="chap6_mj.html#X7A82DC4680DAD67C">6.10-2< diassociative quasigroup <a href="chap7_mj.html#X872DCA027E1A4A1D">7.1-4</a> <br /> <code class="func">DirectProduct</code> <a href="chap4_mj.html#X861BA02C7902A4F4">4.11-1</ <code class="func">Discriminator</code> <a href="chap6_mj.html#X7D09D8957E4A0973">6.11-10< <code class="func">DisplayLibraryInfo</code> <a href="chap9_mj.html#X7A64372E81E713B4">9. distributive quasigroup <a href="chap7_mj.html#X7B76FD6E878ED4F1">7.3-6</a> <br /> left <a href="chap7_mj.html#X7B76FD6E878ED4F1">7.3-6</a> <br /> right <a href="chap7_mj.html#X7B76FD6E878ED4F1">7.3-6</a> <br /> division, left <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> right <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> <code class="func">Elements</code> <a href="chap5_mj.html#X79B130FC7906FB4C">5.1-1</a> <br /> entropic quasigroup <a href="chap7_mj.html#X7F23D4D97A38D223">7.3-7</a> <br /> exact group factorization <a href="chap8_mj.html#X82FC16F386CE11F1">8.1-2</a> <br /> exponent <a href="chap5_mj.html#X7D44470C7DA59C1C">5.1-5</a> <br /> <code class="func">Exponent</code> <a href="chap5_mj.html#X7D44470C7DA59C1C">5.1-5</a> <br /> extension <a href="chap4_mj.html#X8759431780AC81A9">4.8</a> <br /> nuclear <a href="chap4_mj.html#X8759431780AC81A9">4.8</a> <br /> extra loop <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> <code class="func">FactorLoop</code> <a href="chap6_mj.html#X83E1953980E2DE2F">6.8-1</a> <br /> flexible loop <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> folder, quasigroup <a href="chap4_mj.html#X85ABE99E84E5B0E8">4.7</a> <br /> Frattini subloop <a href="chap6_mj.html#X85BD2C517FA7A47E">6.10-4</a> <br /> <code class="func">FrattinifactorSize</code> <a href="chap6_mj.html#X855286367A2D5A54">6. <code class="func">FrattiniSubloop</code> <a href="chap6_mj.html#X85BD2C517FA7A47E">6.10- <code class="func">GeneratorsOfLoop</code> <a href="chap5_mj.html#X83944A777D161D10">5.5- <code class="func">GeneratorsOfQuasigroup</code> <a href="chap5_mj.html#X83944A777D161D1 <code class="func">GeneratorsSmallest</code> <a href="chap5_mj.html#X82FD78AF7F80A0E2">5. group <a href="chap2_mj.html#X80243DE5826583B8">2.1</a> <br /> group with triality <a href="chap8_mj.html#X83E73A767D79FAFD">8.3</a> <br /> groupoid <a href="chap2_mj.html#X80243DE5826583B8">2.1</a> <br /> <code class="func">HasAntiautomorphicInverseProperty</code> <a href="chap7_mj.html#X8538 <code class="func">HasAutomorphicInverseProperty</code> <a href="chap7_mj.html#X7F46CE6B <code class="func">HasInverseProperty</code> <a href="chap7_mj.html#X85EDD10586596458">7. <code class="func">HasLeftInverseProperty</code> <a href="chap7_mj.html#X85EDD1058659645 <code class="func">HasRightInverseProperty</code> <a href="chap7_mj.html#X85EDD105865964 <code class="func">HasTwosidedInverses</code> <a href="chap7_mj.html#X86B93E1B7AEA6EDA">7 <code class="func">HasWeakInverseProperty</code> <a href="chap7_mj.html#X793909B780761EA homomorphism <a href="chap2_mj.html#X791066ED7DD9F254">2.6</a> <br /> homotopism <a href="chap2_mj.html#X791066ED7DD9F254">2.6</a> <br /> idempotent quasigroup <a href="chap7_mj.html#X7CB5896082D29173">7.3-3</a> <br /> identity, element <a href="chap2_mj.html#X80243DE5826583B8">2.1</a> <br /> of Bol-Moufang type <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> inner mapping, left <a href="chap6_mj.html#X8740D61178ACD217">6.5</a> <br /> middle <a href="chap6_mj.html#X8740D61178ACD217">6.5</a> <br /> right <a href="chap6_mj.html#X8740D61178ACD217">6.5</a> <br /> inner mapping group <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> left <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> middle <a href="chap6_mj.html#X8740D61178ACD217">6.5</a> <br /> right <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> <code class="func">InnerMappingGroup</code> <a href="chap6_mj.html#X82513A3B7C3A6420">6.5 <code class="func">InterestingLoop</code> <a href="chap9_mj.html#X87F24AD3811910D3">9.12- <code class="func">IntoGroup</code> <a href="chap4_mj.html#X7B5C6C64831B866E">4.10-4</a> <br /> <code class="func">IntoLoop</code> <a href="chap4_mj.html#X7A59C36683118E5A">4.10-3</a> <br /> <code class="func">IntoQuasigroup</code> <a href="chap4_mj.html#X84575A4B78CC545E">4.10-1< inverse <a href="chap5_mj.html#X810850247ADB4EE9">5.3</a> <br /> <code class="func">Inverse</code> <a href="chap5_mj.html#X805781838020CF44">5.3-1</a> <br /> inverse, left <a href="chap5_mj.html#X810850247ADB4EE9">5.3</a> <a href="chap7_mj.html#X87 right <a href="chap5_mj.html#X810850247ADB4EE9">5.3</a> <a href="chap7_mj.html#X8748BA218 two-sided <a href="chap2_mj.html#X80243DE5826583B8">2.1</a> <a href="chap7_mj.html#X86B93 inverse property <a href="chap7_mj.html#X85EDD10586596458">7.2-1</a> <br /> antiautomorphic <a href="chap7_mj.html#X8538D4638232DB51">7.2-5</a> <br /> automorphic <a href="chap7_mj.html#X7F46CE6B7D387158">7.2-4</a> <br /> left <a href="chap7_mj.html#X85EDD10586596458">7.2-1</a> <br /> right <a href="chap7_mj.html#X85EDD10586596458">7.2-1</a> <br /> weak <a href="chap7_mj.html#X793909B780761EA8">7.2-3</a> <br /> <code class="func">IsALoop</code> <a href="chap7_mj.html#X7899603184CF13FD">7.7-4</a> <br /> <code class="func">IsAlternative</code> <a href="chap7_mj.html#X8379356E82DB5DDA">7.4-15</ <code class="func">IsAssociative</code> <a href="chap7_mj.html#X7C83B5A47FD18FB7">7.1-1</a> < <code class="func">IsAutomorphicLoop</code> <a href="chap7_mj.html#X7899603184CF13FD">7.7 <code class="func">IsCCLoop</code> <a href="chap7_mj.html#X878B614479DCB83F">7.6-3</a> <br /> <code class="func">IsCLoop</code> <a href="chap7_mj.html#X866F04DC7AE54B7C">7.4-3</a> <br /> <code class="func">IsCodeLoop</code> <a href="chap7_mj.html#X790FA1188087D5C1">7.8-1</a> <br /> <code class="func">IsCommutative</code> <a href="chap7_mj.html#X830A4A4C795FBC2D">7.1-2</a> < <code class="func">IsConjugacyClosedLoop</code> <a href="chap7_mj.html#X878B614479DCB83F <code class="func">IsDiassociative</code> <a href="chap7_mj.html#X872DCA027E1A4A1D">7.1-4< <code class="func">IsDistributive</code> <a href="chap7_mj.html#X7B76FD6E878ED4F1">7.3-6</ <code class="func">IsEntropic</code> <a href="chap7_mj.html#X7F23D4D97A38D223">7.3-7</a> <br /> <code class="func">IsExactGroupFactorization</code> <a href="chap8_mj.html#X82FC16F386CE <code class="func">IsExtraLoop</code> <a href="chap7_mj.html#X7988AFE27D06ACB5">7.4-1</a> <br <code class="func">IsFlexible</code> <a href="chap7_mj.html#X7C32851A7AF1C45F">7.4-12</a> <br <code class="func">IsIdempotent</code> <a href="chap7_mj.html#X7CB5896082D29173">7.3-3</a> <b <code class="func">IsLCCLoop</code> <a href="chap7_mj.html#X784E08CD7B710AF4">7.6-1</a> <br /> <code class="func">IsLCLoop</code> <a href="chap7_mj.html#X789E0A6979697C4C">7.4-6</a> <br /> <code class="func">IsLeftALoop</code> <a href="chap7_mj.html#X7F063914804659F1">7.7-1</a> <br <code class="func">IsLeftAlternative</code> <a href="chap7_mj.html#X7DF0196786B9CE08">7.4 <code class="func">IsLeftAutomorphicLoop</code> <a href="chap7_mj.html#X7F063914804659F1 <code class="func">IsLeftBolLoop</code> <a href="chap7_mj.html#X801DAAE8834A1A65">7.4-4</a> < <code class="func">IsLeftBruckLoop</code> <a href="chap7_mj.html#X85F1BD4280E44F5B">7.8-3< <code class="func">IsLeftConjugacyClosedLoop</code> <a href="chap7_mj.html#X784E08CD7B71 <code class="func">IsLeftDistributive</code> <a href="chap7_mj.html#X7B76FD6E878ED4F1">7. <code class="func">IsLeftKLoop</code> <a href="chap7_mj.html#X85F1BD4280E44F5B">7.8-3</a> <br <code class="func">IsLeftNuclearSquareLoop</code> <a href="chap7_mj.html#X819F285887B5EB <code class="func">IsLeftPowerAlternative</code> <a href="chap7_mj.html#X875C3DF681B3FAE IsLoop <a href="chap3_mj.html#X86F02BBD87FEA1C6">3.1</a> <br /> <code class="func">IsLoopCayleyTable</code> <a href="chap4_mj.html#X7AAE48507A471069">4.2 IsLoopElement <a href="chap3_mj.html#X86F02BBD87FEA1C6">3.1</a> <br /> <code class="func">IsLoopTable</code> <a href="chap4_mj.html#X7AAE48507A471069">4.2-2</a> <br <code class="func">IsMedial</code> <a href="chap7_mj.html#X7F23D4D97A38D223">7.3-7</a> <br /> <code class="func">IsMiddleALoop</code> <a href="chap7_mj.html#X7DFE830584A769E5">7.7-2</a> < <code class="func">IsMiddleAutomorphicLoop</code> <a href="chap7_mj.html#X7DFE830584A769 <code class="func">IsMiddleNuclearSquareLoop</code> <a href="chap7_mj.html#X8474F5568124 <code class="func">IsMoufangLoop</code> <a href="chap7_mj.html#X7F1C151484C97E61">7.4-2</a> < <code class="func">IsNilpotent</code> <a href="chap6_mj.html#X78A4B93781C96AAE">6.9-1</a> <br <code class="func">IsNormal</code> <a href="chap6_mj.html#X838186F9836F678C">6.7-1</a> <br /> <code class="func">IsNuclearSquareLoop</code> <a href="chap7_mj.html#X796650088213229B">7 <code class="func">IsomorphicCopyByNormalSubloop</code> <a href="chap6_mj.html#X8121DE3A <code class="func">IsomorphicCopyByPerm</code> <a href="chap6_mj.html#X85B3E22679FD8D81"> isomorphism <a href="chap2_mj.html#X791066ED7DD9F254">2.6</a> <br /> <code class="func">IsomorphismLoops</code> <a href="chap6_mj.html#X7D7B10D6836FCA9F">6.11 <code class="func">IsomorphismQuasigroups</code> <a href="chap6_mj.html#X801067F67E5292F <code class="func">IsOsbornLoop</code> <a href="chap7_mj.html#X8655956878205FC1">7.6-4</a> <b isotopism <a href="chap2_mj.html#X791066ED7DD9F254">2.6</a> <br /> principal <a href="chap2_mj.html#X791066ED7DD9F254">2.6</a> <br /> <code class="func">IsotopismLoops</code> <a href="chap6_mj.html#X84C5ADE77F910F63">6.12-1< <code class="func">IsPowerAlternative</code> <a href="chap7_mj.html#X875C3DF681B3FAE2">7. <code class="func">IsPowerAssociative</code> <a href="chap7_mj.html#X7D53EA947F1CDA69">7. IsQuasigroup <a href="chap3_mj.html#X86F02BBD87FEA1C6">3.1</a> <br /> <code class="func">IsQuasigroupCayleyTable</code> <a href="chap4_mj.html#X81179355869B9D IsQuasigroupElement <a href="chap3_mj.html#X86F02BBD87FEA1C6">3.1</a> <br /> <code class="func">IsQuasigroupTable</code> <a href="chap4_mj.html#X81179355869B9DFE">4.2 <code class="func">IsRCCLoop</code> <a href="chap7_mj.html#X7B3016B47A1A8213">7.6-2</a> <br /> <code class="func">IsRCLoop</code> <a href="chap7_mj.html#X7B03CC577802F4AB">7.4-7</a> <br /> <code class="func">IsRightALoop</code> <a href="chap7_mj.html#X7EA9165A87F99E35">7.7-3</a> <b <code class="func">IsRightAlternative</code> <a href="chap7_mj.html#X8416FAD87F148F5D">7. <code class="func">IsRightAutomorphicLoop</code> <a href="chap7_mj.html#X7EA9165A87F99E3 <code class="func">IsRightBolLoop</code> <a href="chap7_mj.html#X79279F9787E72566">7.4-5</ <code class="func">IsRightBruckLoop</code> <a href="chap7_mj.html#X857B373E7B4E0519">7.8- <code class="func">IsRightConjugacyClosedLoop</code> <a href="chap7_mj.html#X7B3016B47A1 <code class="func">IsRightDistributive</code> <a href="chap7_mj.html#X7B76FD6E878ED4F1">7 <code class="func">IsRightKLoop</code> <a href="chap7_mj.html#X857B373E7B4E0519">7.8-4</a> <b <code class="func">IsRightNuclearSquareLoop</code> <a href="chap7_mj.html#X807B3B21825E3 <code class="func">IsRightPowerAlternative</code> <a href="chap7_mj.html#X875C3DF681B3FA <code class="func">IsSemisymmetric</code> <a href="chap7_mj.html#X834848ED85F9012B">7.3-1< <code class="func">IsSimple</code> <a href="chap6_mj.html#X7D8E63A7824037CC">6.7-3</a> <br /> <code class="func">IsSolvable</code> <a href="chap6_mj.html#X79B10B337A3B1C6E">6.10-1</a> <br <code class="func">IsSteinerLoop</code> <a href="chap7_mj.html#X793600C9801F4F62">7.8-2</a> < <code class="func">IsSteinerQuasigroup</code> <a href="chap7_mj.html#X83DE7DD77C056C1F">7 <code class="func">IsStronglyNilpotent</code> <a href="chap6_mj.html#X7E7C2D117B55F6A0">6 <code class="func">IsSubloop</code> <a href="chap6_mj.html#X87AC8B7E80CE9260">6.2-3</a> <br /> <code class="func">IsSubquasigroup</code> <a href="chap6_mj.html#X87AC8B7E80CE9260">6.2-3< <code class="func">IsTotallySymmetric</code> <a href="chap7_mj.html#X834F809B8060B754">7. <code class="func">IsUnipotent</code> <a href="chap7_mj.html#X7CA3DCA07B6CB9BD">7.3-5</a> <br <code class="func">ItpSmallLoop</code> <a href="chap9_mj.html#X850C4C01817A098D">9.13-1</a> < K loop, left <a href="chap7_mj.html#X85F1BD4280E44F5B">7.8-3</a> <br /> right <a href="chap7_mj.html#X857B373E7B4E0519">7.8-4</a> <br /> latin square <a href="chap2_mj.html#X80243DE5826583B8">2.1</a> <a href="chap4_mj.html#X7DE random <a href="chap4_mj.html#X7AE29A1A7AA5C25A">4.9</a> <br /> LC loop <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> <code class="func">LCCLoop</code> <a href="chap9_mj.html#X80AB8B107D55FB19">9.7-2</a> <br /> <code class="func">LeftBolLoop</code> <a href="chap9_mj.html#X7EE99F647C537994">9.2-1</a> <br <code class="func">LeftBruckLoop</code> <a href="chap9_mj.html#X8290B01780F0FCD3">9.3-1</a> < <code class="func">LeftConjugacyClosedLoop</code> <a href="chap9_mj.html#X80AB8B107D55FB <code class="func">LeftDivision</code> <a href="chap5_mj.html#X7D5956967BCC1834">5.2-1</a> <a <code class="func">LeftDivisionCayleyTable</code> <a href="chap5_mj.html#X804F67C8796A0E <code class="func">LeftInnerMapping</code> <a href="chap6_mj.html#X7EE1E78C856C6F7C">6.5- <code class="func">LeftInnerMappingGroup</code> <a href="chap6_mj.html#X79CDA09A7D48BF2B <code class="func">LeftInverse</code> <a href="chap5_mj.html#X805781838020CF44">5.3-1</a> <br <code class="func">LeftMultiplicationGroup</code> <a href="chap6_mj.html#X7AB8C9947C1303 <code class="func">LeftNucleus</code> <a href="chap6_mj.html#X798316F47A47FF63">6.6-1</a> <br <code class="func">LeftSection</code> <a href="chap6_mj.html#X7EB9197C80FB4664">6.3-2</a> <br <code class="func">LeftTranslation</code> <a href="chap6_mj.html#X7B45B48C7C4D6061">6.3-1< <code class="func">LibraryLoop</code> <a href="chap9_mj.html#X849865D6786EEF9B">9.1-1</a> <br License <a href="chap0_mj.html#X81488B807F2A1CF1">.-2</a> <br /> loop <a href="chap2_mj.html#X80243DE5826583B8">2.1</a> <br /> alternative <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> associated left Bruck <a href="chap8_mj.html#X8664CA927DD73DBE">8.1-1</a> <br /> automorphic <a href="chap7_mj.html#X793B22EA8643C667">7.7</a> <br /> C <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> Chein <a href="chap8_mj.html#X7CC6CDB786E9BBA0">8.2-3</a> <br /> code <a href="chap7_mj.html#X790FA1188087D5C1">7.8-1</a> <br /> conjugacy closed <a href="chap7_mj.html#X8176B2C47A4629CD">7.6</a> <br /> extra <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> flexible <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> LC <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> left alternative <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> left automorphic <a href="chap7_mj.html#X793B22EA8643C667">7.7</a> <br /> left Bol <a href="chap3_mj.html#X87E49ED884FA6DC4">3.3</a> <a href="chap7_mj.html#X780D907 left Bruck <a href="chap7_mj.html#X85F1BD4280E44F5B">7.8-3</a> <br /> left conjugacy closed <a href="chap7_mj.html#X8176B2C47A4629CD">7.6</a> <br /> left K <a href="chap7_mj.html#X85F1BD4280E44F5B">7.8-3</a> <br /> left nuclear square <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> left power alternative <a href="chap7_mj.html#X83A501387E1AC371">7.5</a> <br /> middle automorphic <a href="chap7_mj.html#X793B22EA8643C667">7.7</a> <br /> middle nuclear square <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> Moufang <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> nilpotent <a href="chap2_mj.html#X869CBCE381E2C422">2.4</a> <a href="chap4_mj.html#X81713 nuclear square <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> octonion <a href="chap9_mj.html#X81E82098822543EE">9.4-1</a> <br /> of Bol-Moufang type <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> Osborn <a href="chap7_mj.html#X8655956878205FC1">7.6-4</a> <br /> Paige <a href="chap9_mj.html#X8135C8FD8714C606">9.9</a> <br /> power alternative <a href="chap7_mj.html#X83A501387E1AC371">7.5</a> <br /> power associative <a href="chap5_mj.html#X7D44470C7DA59C1C">5.1-5</a> <br /> RC <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> right alternative <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> right automorphic <a href="chap7_mj.html#X793B22EA8643C667">7.7</a> <br /> right Bol <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> right Bruck <a href="chap7_mj.html#X857B373E7B4E0519">7.8-4</a> <br /> right conjugacy closed <a href="chap7_mj.html#X8176B2C47A4629CD">7.6</a> <br /> right K <a href="chap7_mj.html#X857B373E7B4E0519">7.8-4</a> <br /> right nuclear square <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> right power alternative <a href="chap7_mj.html#X83A501387E1AC371">7.5</a> <br /> sedenion <a href="chap9_mj.html#X843BD73F788049F7">9.12</a> <br /> simple <a href="chap3_mj.html#X87E49ED884FA6DC4">3.3</a> <a href="chap6_mj.html#X7D8E63A7 solvable <a href="chap2_mj.html#X869CBCE381E2C422">2.4</a> <br /> Steiner <a href="chap7_mj.html#X793600C9801F4F62">7.8-2</a> <br /> strongly nilpotent <a href="chap6_mj.html#X7E7C2D117B55F6A0">6.9-3</a> <br /> loop isotope, principal <a href="chap2_mj.html#X791066ED7DD9F254">2.6</a> <br /> loop table <a href="chap4_mj.html#X7DE8405B82BC36A9">4.1</a> <br /> <code class="func">LoopByCayleyTable</code> <a href="chap4_mj.html#X860135BB85F2DB19">4.4 <code class="func">LoopByCyclicModification</code> <a href="chap8_mj.html#X7B3165C083709 <code class="func">LoopByDihedralModification</code> <a href="chap8_mj.html#X7D7717C587B <code class="func">LoopByExtension</code> <a href="chap4_mj.html#X79AEE93E7E15B802">4.8-2< <code class="func">LoopByLeftSection</code> <a href="chap4_mj.html#X7EC1EB0D7B8382A1">4.6 <code class="func">LoopByRightFolder</code> <a href="chap4_mj.html#X83168E62861F70AB">4.7 <code class="func">LoopByRightSection</code> <a href="chap4_mj.html#X80B436ED7CC0749E">4. <code class="func">LoopFromFile</code> <a href="chap4_mj.html#X81A1DB918057933E">4.5-1</a> <b <code class="func">LoopIsomorph</code> <a href="chap6_mj.html#X7BD1AC32851286EA">6.11-7</a> < <code class="func">LoopMG2</code> <a href="chap8_mj.html#X7CC6CDB786E9BBA0">8.2-3</a> <br /> <code class="func">LoopsUpToIsomorphism</code> <a href="chap6_mj.html#X8308F38283C61B20"> <code class="func">LoopsUpToIsotopism</code> <a href="chap6_mj.html#X841E540B7A7EF29F">6. <code class="func">LowerCentralSeries</code> <a href="chap6_mj.html#X817BDBC2812992ED">6. magma <a href="chap2_mj.html#X80243DE5826583B8">2.1</a> <br /> medial quasigroup <a href="chap7_mj.html#X7F23D4D97A38D223">7.3-7</a> <br /> <code class="func">MiddleInnerMapping</code> <a href="chap6_mj.html#X7EE1E78C856C6F7C">6. <code class="func">MiddleInnerMappingGroup</code> <a href="chap6_mj.html#X79CDA09A7D48BF <code class="func">MiddleNucleus</code> <a href="chap6_mj.html#X798316F47A47FF63">6.6-1</a> < modification, cyclic <a href="chap8_mj.html#X7B3165C083709831">8.2-1</a> <br /> dihedral <a href="chap8_mj.html#X7D7717C587BC2D1E">8.2-2</a> <br /> Moufang <a href="chap8_mj.html#X819F82737C2A860D">8.2</a> <br /> Moufang loop <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> <code class="func">MoufangLoop</code> <a href="chap9_mj.html#X81E82098822543EE">9.4-1</a> <br multiplication group <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> left <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> relative <a href="chap6_mj.html#X847256B779E1E7E5">6.4-2</a> <br /> relative left <a href="chap6_mj.html#X847256B779E1E7E5">6.4-2</a> <br /> relative right <a href="chap6_mj.html#X847256B779E1E7E5">6.4-2</a> <br /> right <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> multiplication table <a href="chap4_mj.html#X7DE8405B82BC36A9">4.1</a> <br /> <code class="func">MultiplicationGroup</code> <a href="chap6_mj.html#X7AB8C9947C1303E2">6 <code class="func">MyLibraryLoop</code> <a href="chap9_mj.html#X78C4B8757902D49F">9.1-2</a> < <code class="func">NaturalHomomorphismByNormalSubloop</code> <a href="chap6_mj.html#X870 neutral element <a href="chap2_mj.html#X80243DE5826583B8">2.1</a> <br /> nilpotence class <a href="chap2_mj.html#X869CBCE381E2C422">2.4</a> <br /> <code class="func">NilpotencyClassOfLoop</code> <a href="chap6_mj.html#X7D5FC62581A99482 nilpotent loop <a href="chap2_mj.html#X869CBCE381E2C422">2.4</a> <br /> strongly <a href="chap6_mj.html#X7E7C2D117B55F6A0">6.9-3</a> <br /> <code class="func">NilpotentLoop</code> <a href="chap9_mj.html#X7A9C960D86E2AD28">9.10-1</ normal closure <a href="chap6_mj.html#X7BDEA0A98720D1BB">6.7-2</a> <br /> normal subloop <a href="chap6_mj.html#X838186F9836F678C">6.7-1</a> <br /> <code class="func">NormalClosure</code> <a href="chap6_mj.html#X7BDEA0A98720D1BB">6.7-2</a> < <code class="func">NormalizedQuasigroupTable</code> <a href="chap4_mj.html#X821A2F9E85FA <code class="func">Nuc</code> <a href="chap6_mj.html#X84D389677A91C290">6.6-2</a> <br /> nuclear square loop <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> left <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> middle <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> right <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> <code class="func">NuclearExtension</code> <a href="chap4_mj.html#X784733C67AA6B2FA">4.8- nucleus <a href="chap2_mj.html#X83EDF04F7952143F">2.3</a> <br /> left <a href="chap2_mj.html#X83EDF04F7952143F">2.3</a> <br /> middle <a href="chap2_mj.html#X83EDF04F7952143F">2.3</a> <br /> right <a href="chap2_mj.html#X83EDF04F7952143F">2.3</a> <br /> <code class="func">NucleusOfLoop</code> <a href="chap6_mj.html#X84D389677A91C290">6.6-2</a> < <code class="func">NucleusOfQuasigroup</code> <a href="chap6_mj.html#X84D389677A91C290">6 octonion loop <a href="chap9_mj.html#X81E82098822543EE">9.4-1</a> <br /> <code class="func">One</code> <a href="chap5_mj.html#X8129A6877FFD804B">5.1-3</a> <br /> <code class="func">OneLoopTableInGroup</code> <a href="chap8_mj.html#X7BFFC66A824BA6AA">8 <code class="func">OneLoopWithMltGroup</code> <a href="chap8_mj.html#X8266DE05824226E6">8 <code class="func">OneProperLoopTableInGroup</code> <a href="chap8_mj.html#X84C5A76585B3 <code class="func">Opposite</code> <a href="chap4_mj.html#X87B6AED47EE2BCD3">4.12-1</a> <br /> opposite quasigroup <a href="chap4_mj.html#X7865FC8D7854C2E3">4.12</a> <br /> <code class="func">OppositeLoop</code> <a href="chap4_mj.html#X87B6AED47EE2BCD3">4.12-1</a> < <code class="func">OppositeQuasigroup</code> <a href="chap4_mj.html#X87B6AED47EE2BCD3">4. Osborn loop <a href="chap7_mj.html#X8655956878205FC1">7.6-4</a> <br /> Paige loop <a href="chap9_mj.html#X8135C8FD8714C606">9.9</a> <br /> <code class="func">PaigeLoop</code> <a href="chap9_mj.html#X7FCF4D6B7AD66D74">9.9-1</a> <br /> <code class="func">Parent</code> <a href="chap6_mj.html#X7BC856CC7F116BB0">6.1-1</a> <br /> <code class="func">PosInParent</code> <a href="chap6_mj.html#X832295DE866E44EE">6.1-3</a> <br <code class="func">Position</code> <a href="chap6_mj.html#X79975EC6783B4293">6.1-2</a> <br /> power alternative loop <a href="chap7_mj.html#X83A501387E1AC371">7.5</a> <br /> left <a href="chap7_mj.html#X83A501387E1AC371">7.5</a> <br /> right <a href="chap7_mj.html#X83A501387E1AC371">7.5</a> <br /> power associative loop <a href="chap5_mj.html#X7D44470C7DA59C1C">5.1-5</a> <br /> power associative quasigroup <a href="chap7_mj.html#X7D53EA947F1CDA69">7.1-3</a> <br /> <code class="func">PrincipalLoopIsotope</code> <a href="chap4_mj.html#X79CEA57C850C7070"> quasigroup <a href="chap2_mj.html#X80243DE5826583B8">2.1</a> <br /> diassociative <a href="chap7_mj.html#X872DCA027E1A4A1D">7.1-4</a> <br /> distributive <a href="chap7_mj.html#X7B76FD6E878ED4F1">7.3-6</a> <br /> entropic <a href="chap7_mj.html#X7F23D4D97A38D223">7.3-7</a> <br /> idempotent <a href="chap7_mj.html#X7CB5896082D29173">7.3-3</a> <br /> left distributive <a href="chap7_mj.html#X7B76FD6E878ED4F1">7.3-6</a> <br /> medial <a href="chap7_mj.html#X7F23D4D97A38D223">7.3-7</a> <br /> opposite <a href="chap4_mj.html#X7865FC8D7854C2E3">4.12</a> <br /> power associative <a href="chap7_mj.html#X7D53EA947F1CDA69">7.1-3</a> <br /> right distributive <a href="chap7_mj.html#X7B76FD6E878ED4F1">7.3-6</a> <br /> semisymmetric <a href="chap7_mj.html#X834848ED85F9012B">7.3-1</a> <br /> Steiner <a href="chap7_mj.html#X83DE7DD77C056C1F">7.3-4</a> <br /> totally symmetric <a href="chap7_mj.html#X834F809B8060B754">7.3-2</a> <br /> unipotent <a href="chap7_mj.html#X7CA3DCA07B6CB9BD">7.3-5</a> <br /> quasigroup table <a href="chap4_mj.html#X7DE8405B82BC36A9">4.1</a> <br /> <code class="func">QuasigroupByCayleyTable</code> <a href="chap4_mj.html#X860135BB85F2DB <code class="func">QuasigroupByLeftSection</code> <a href="chap4_mj.html#X7EC1EB0D7B8382 <code class="func">QuasigroupByRightFolder</code> <a href="chap4_mj.html#X83168E62861F70 <code class="func">QuasigroupByRightSection</code> <a href="chap4_mj.html#X80B436ED7CC07 <code class="func">QuasigroupFromFile</code> <a href="chap4_mj.html#X81A1DB918057933E">4. <code class="func">QuasigroupIsomorph</code> <a href="chap6_mj.html#X7A42812B7B027DD4">6. <code class="func">QuasigroupsUpToIsomorphism</code> <a href="chap6_mj.html#X82373C54795 <code class="func">RandomLoop</code> <a href="chap4_mj.html#X8271C0F5786B6FA9">4.9-1</a> <br /> <code class="func">RandomNilpotentLoop</code> <a href="chap4_mj.html#X817132C887D3FD3A">4 <code class="func">RandomQuasigroup</code> <a href="chap4_mj.html#X8271C0F5786B6FA9">4.9- RC loop <a href="chap7_mj.html#X780D907986EBA6C7">7.4</a> <br /> <code class="func">RCCLoop</code> <a href="chap9_mj.html#X806B2DE67990E42F">9.7-1</a> <br /> <code class="func">RelativeLeftMultiplicationGroup</code> <a href="chap6_mj.html#X847256 <code class="func">RelativeMultiplicationGroup</code> <a href="chap6_mj.html#X847256B779 <code class="func">RelativeRightMultiplicationGroup</code> <a href="chap6_mj.html#X84725 <code class="func">RightBolLoop</code> <a href="chap9_mj.html#X8774304282654C58">9.2-2</a> <b <code class="func">RightBolLoopByExactGroupFactorization</code> <a href="chap8_mj.html#X <code class="func">RightBruckLoop</code> <a href="chap9_mj.html#X798DD7CF871F648F">9.3-2</ <code class="func">RightConjugacyClosedLoop</code> <a href="chap9_mj.html#X806B2DE67990E <code class="func">RightCosets</code> <a href="chap6_mj.html#X835F48248571364F">6.2-6</a> <br <code class="func">RightDivision</code> <a href="chap5_mj.html#X7D5956967BCC1834">5.2-1</a> < <code class="func">RightDivisionCayleyTable</code> <a href="chap5_mj.html#X804F67C8796A0 <code class="func">RightInnerMapping</code> <a href="chap6_mj.html#X7EE1E78C856C6F7C">6.5 <code class="func">RightInnerMappingGroup</code> <a href="chap6_mj.html#X79CDA09A7D48BF2 <code class="func">RightInverse</code> <a href="chap5_mj.html#X805781838020CF44">5.3-1</a> <b <code class="func">RightMultiplicationGroup</code> <a href="chap6_mj.html#X7AB8C9947C130 <code class="func">RightNucleus</code> <a href="chap6_mj.html#X798316F47A47FF63">6.6-1</a> <b <code class="func">RightSection</code> <a href="chap6_mj.html#X7EB9197C80FB4664">6.3-2</a> <b <code class="func">RightTranslation</code> <a href="chap6_mj.html#X7B45B48C7C4D6061">6.3- <code class="func">RightTransversal</code> <a href="chap6_mj.html#X85C65D06822E716F">6.2- section, left <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> right <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> sedenion loop <a href="chap9_mj.html#X843BD73F788049F7">9.12</a> <br /> semisymmetric quasigroup <a href="chap7_mj.html#X834848ED85F9012B">7.3-1</a> <br /> <code class="func">SetLoopElmName</code> <a href="chap3_mj.html#X7A7EB1B579273D07">3.4-1</ <code class="func">SetQuasigroupElmName</code> <a href="chap3_mj.html#X7A7EB1B579273D07"> simple loop <a href="chap3_mj.html#X87E49ED884FA6DC4">3.3</a> <a href="chap6_mj.html#X7D8E <code class="func">Size</code> <a href="chap5_mj.html#X858ADA3B7A684421">5.1-4</a> <br /> <code class="func">SmallGeneratingSet</code> <a href="chap5_mj.html#X814DBABC878D5232">5. <code class="func">SmallLoop</code> <a href="chap9_mj.html#X7C6EE23E84CD87D3">9.8-1</a> <br /> solvability class <a href="chap2_mj.html#X869CBCE381E2C422">2.4</a> <br /> solvable loop <a href="chap2_mj.html#X869CBCE381E2C422">2.4</a> <br /> Steiner loop <a href="chap7_mj.html#X793600C9801F4F62">7.8-2</a> <br /> Steiner quasigroup <a href="chap7_mj.html#X83DE7DD77C056C1F">7.3-4</a> <br /> <code class="func">SteinerLoop</code> <a href="chap9_mj.html#X87C235457E859AF4">9.6-1</a> <br strongly nilpotent loop <a href="chap6_mj.html#X7E7C2D117B55F6A0">6.9-3</a> <br /> subloop <a href="chap2_mj.html#X83EDF04F7952143F">2.3</a> <br /> <code class="func">Subloop</code> <a href="chap6_mj.html#X84E6744E804AE830">6.2-2</a> <br /> subloop, normal <a href="chap2_mj.html#X83EDF04F7952143F">2.3</a> <a href="chap6_mj.html#X subquasigroup <a href="chap2_mj.html#X83EDF04F7952143F">2.3</a> <br /> <code class="func">Subquasigroup</code> <a href="chap6_mj.html#X7DD511FF864FCDFF">6.2-1</a> < totally symmetric quasigroup <a href="chap7_mj.html#X834F809B8060B754">7.3-2</a> <br /> translation, left <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> right <a href="chap2_mj.html#X7EC01B437CC2B2C9">2.2</a> <br /> transversal <a href="chap6_mj.html#X85C65D06822E716F">6.2-7</a> <br /> <code class="func">TrialityPcGroup</code> <a href="chap8_mj.html#X82CC977085DFDFE8">8.3-2< <code class="func">TrialityPermGroup</code> <a href="chap8_mj.html#X7DB4DE647F6F56F0">8.3 unipotent quasigroup <a href="chap7_mj.html#X7CA3DCA07B6CB9BD">7.3-5</a> <br /> <code class="func">UpperCentralSeries</code> <a href="chap6_mj.html#X7ED37AA07BEE79E0">6. <p> </p> </div> <div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a> <a href="chap0_mj.ht <div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top< <hr /> <p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GA </body> </html>
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