\indexentry {Installation@Installation|indexit}{5}
\indexentry {Documentation@Documentation|indexit}{5}
\indexentry {Test files@Test files|indexit}{5}
\indexentry {Feedback@Feedback|indexit}{5}
\indexentry {Acknowledgement@Acknowledgement|indexit}{5}
\indexentry {Quasigroups and loops@Quasigroups and loops|indexit}{6}
\indexentry {groupoid}{6}
\indexentry {magma}{6}
\indexentry {semigroup}{6}
\indexentry {neutral element}{6}
\indexentry {identity element}{6}
\indexentry {monoid}{6}
\indexentry {inverse!two-sided}{6}
\indexentry {group}{6}
\indexentry {quasigroup}{6}
\indexentry {Latin square}{6}
\indexentry {loop}{6}
\indexentry {Translations@Translations|indexit}{6}
\indexentry {translation!left}{6}
\indexentry {translation!right}{6}
\indexentry {section!left}{6}
\indexentry {section!right}{6}
\indexentry {multiplication group!left}{6}
\indexentry {multiplication group!right}{6}
\indexentry {multiplication group}{6}
\indexentry {Homomorphisms and homotopisms@Homomorphisms and homotopisms|indexit}{6}
\indexentry {homomorphism}{6}
\indexentry {isomorphism}{6}
\indexentry {homotopism}{6}
\indexentry {isotopism}{6}
\indexentry {isotopism!principal}{6}
\indexentry {loop isotope!principal}{6}
\indexentry {Extensions@Extensions|indexit}{6}
\indexentry {extension}{6}
\indexentry {extension!nuclear}{6}
\indexentry {cocycle}{7}
\indexentry {Representing quasigroups@Representing quasigroups|indexit}{8}
\indexentry {Conversions between magmas, quasigroups, loops and groups@Conversions between magmas, quasigroups, loops and groups|indexit}{8}
\indexentry {Calculating with quasigroups@Calculating with quasigroups|indexit}{9}
\indexentry {Bol loop}{9}
\indexentry {loop!Bol}{9}
\indexentry {simple loop}{9}
\indexentry {loop!simple}{9}
\indexentry {Naming, viewing and printing quasigroups and their elements@Naming, viewing and printing quasigroups and their elements|indexit}{9}
\indexentry {SetQuasigroupElmName@`SetQuasigroupElmName'}{10}
\indexentry {SetLoopElmName@`SetLoopElmName'}{10}
\indexentry {About Cayley tables@About Cayley tables|indexit}{11}
\indexentry {table!Cayley}{11}
\indexentry {Cayley table}{11}
\indexentry {table!multiplication}{11}
\indexentry {multiplication table}{11}
\indexentry {table!quasigroup}{11}
\indexentry {quasigroup!table}{11}
\indexentry {Latin square}{11}
\indexentry {table!loop}{11}
\indexentry {loop!table}{11}
\indexentry {Testing Cayley tables@Testing Cayley tables|indexit}{11}
\indexentry {IsQuasigroupTable@`IsQuasigroupTable'}{11}
\indexentry {IsQuasigroupCayleyTable@`IsQuasigroupCayleyTable'}{11}
\indexentry {IsLoopTable@`IsLoopTable'}{11}
\indexentry {IsLoopCayleyTable@`IsLoopCayleyTable'}{11}
\indexentry {Canonical and normalized Cayley tables@Canonical and normalized Cayley tables|indexit}{11}
\indexentry {CanonicalCayleyTable@`CanonicalCayleyTable'}{11}
\indexentry {NormalizedQuasigroupTable@`NormalizedQuasigroupTable'}{11}
\indexentry {Creating quasigroups and loops manually@Creating quasigroups and loops manually|indexit}{11}
\indexentry {QuasigroupByCayleyTable@`QuasigroupByCayleyTable'}{12}
\indexentry {LoopByCayleyTable@`LoopByCayleyTable'}{12}
\indexentry {Creating quasigroups and loops from a file@Creating quasigroups and loops from a file|indexit}{12}
\indexentry {QuasigroupFromFile@`QuasigroupFromFile'}{12}
\indexentry {LoopFromFile@`LoopFromFile'}{12}
\indexentry {Creating quasigroups and loops by sections@Creating quasigroups and loops by sections|indexit}{13}
\indexentry {CayleyTableByPerms@`CayleyTableByPerms'}{13}
\indexentry {QuasigroupByLeftSection@`QuasigroupByLeftSection'}{13}
\indexentry {LoopByLeftSection@`LoopByLeftSection'}{13}
\indexentry {QuasigroupByRightSection@`QuasigroupByRightSection'}{13}
\indexentry {LoopByRightSection@`LoopByRightSection'}{13}
\indexentry {transversal}{13}
\indexentry {QuasigroupByRightSection@`QuasigroupByRightSection'}{13}
\indexentry {LoopByRightSection@`LoopByRightSection'}{13}
\indexentry {Bol loop!simple}{13}
\indexentry {simple loop!Bol}{13}
\indexentry {Creating quasigroups and loops by extensions@Creating quasigroups and loops by extensions|indexit}{14}
\indexentry {NuclearExtension@`NuclearExtension'}{14}
\indexentry {LoopByExtension@`LoopByExtension'}{14}
\indexentry {Random quasigroups and loops@Random quasigroups and loops|indexit}{14}
\indexentry {Latin square!random}{14}
\indexentry {random!loop}{14}
\indexentry {loop!random}{14}
\indexentry {RandomLoop@`RandomLoop'}{14}
\indexentry {RandomLoop@`RandomLoop'}{15}
\indexentry {quasigroup!random}{15}
\indexentry {random!quasigroup}{15}
\indexentry {RandomQuasigroup@`RandomQuasigroup'}{15}
\indexentry {RandomQuasigroup@`RandomQuasigroup'}{15}
\indexentry {RandomNilpotentLoop@`RandomNilpotentLoop'}{15}
\indexentry {nilpotent loop!random}{15}
\indexentry {random!nilpotent loop}{15}
\indexentry {Conversions@Conversions|indexit}{15}
\indexentry {IntoQuasigroup@`IntoQuasigroup'}{15}
\indexentry {PrincipalLoopIsotope@`PrincipalLoopIsotope'}{15}
\indexentry {IntoLoop@`IntoLoop'}{15}
\indexentry {IntoGroup@`IntoGroup'}{15}
\indexentry {Products of loops@Products of loops|indexit}{16}
\indexentry {DirectProduct@`DirectProduct'}{16}
\indexentry {Opposite quasigroups and loops@Opposite quasigroups and loops|indexit}{16}
\indexentry {opposite quasigroup}{16}
\indexentry {quasigroup!opposite}{16}
\indexentry {Opposite@`Opposite'}{16}
\indexentry {Basic attributes@Basic attributes|indexit}{17}
\indexentry {Elements@`Elements'}{17}
\indexentry {CayleyTable@`CayleyTable'}{17}
\indexentry {One@`One'}{17}
\indexentry {MultiplicativeNeutralElement@`MultiplicativeNeutralElement'}{17}
\indexentry {Size@`Size'}{17}
\indexentry {power associative!loop}{17}
\indexentry {loop!power associative}{17}
\indexentry {exponent}{17}
\indexentry {Exponent@`Exponent'}{17}
\indexentry {Basic arithmetic operations@Basic arithmetic operations|indexit}{17}
\indexentry {division!left}{17}
\indexentry {division!right}{17}
\indexentry {LeftDivision@`LeftDivision'}{17}
\indexentry {RightDivision@`RightDivision'}{17}
\indexentry {LeftDivision@`LeftDivision'}{17}
\indexentry {LeftDivision@`LeftDivision'}{17}
\indexentry {RightDivision@`RightDivision'}{17}
\indexentry {RightDivision@`RightDivision'}{17}
\indexentry {LeftDivisionCayleyTable@`LeftDivisionCayleyTable'}{18}
\indexentry {RightDivisionCayleyTable@`RightDivisionCayleyTable'}{18}
\indexentry {Powers and inverses@Powers and inverses|indexit}{18}
\indexentry {power associative!quasigroup}{18}
\indexentry {quasigroup!power associative}{18}
\indexentry {inverse!left}{18}
\indexentry {inverse!right}{18}
\indexentry {inverse}{18}
\indexentry {LeftInverse@`LeftInverse'}{18}
\indexentry {RightInverse@`RightInverse'}{18}
\indexentry {Inverse@`Inverse'}{18}
\indexentry {Associators and commutators@Associators and commutators|indexit}{18}
\indexentry {associator}{18}
\indexentry {commutator}{18}
\indexentry {Associator@`Associator'}{18}
\indexentry {Commutator@`Commutator'}{18}
\indexentry {Generators@Generators|indexit}{18}
\indexentry {GeneratorsOfQuasigroup@`GeneratorsOfQuasigroup'}{18}
\indexentry {GeneratorsOfLoop@`GeneratorsOfLoop'}{18}
\indexentry {GeneratorsSmallest@`GeneratorsSmallest'}{18}
\indexentry {Parent of a quasigroup@Parent of a quasigroup|indexit}{19}
\indexentry {Parent@`Parent'}{19}
\indexentry {Position@`Position'}{19}
\indexentry {PosInParent@`PosInParent'}{19}
\indexentry {Comparing quasigroups with common parent@Comparing quasigroups with common parent|indexit}{19}
\indexentry {Subquasigroups and subloops@Subquasigroups and subloops|indexit}{19}
\indexentry {Subquasigroup@`Subquasigroup'}{19}
\indexentry {Subloop@`Subloop'}{19}
\indexentry {IsSubquasigroup@`IsSubquasigroup'}{20}
\indexentry {IsSubloop@`IsSubloop'}{20}
\indexentry {AllSubloops@`AllSubloops'}{20}
\indexentry {coset}{20}
\indexentry {RightCosets@`RightCosets'}{20}
\indexentry {transversal}{20}
\indexentry {RightTransversal@`RightTransversal'}{20}
\indexentry {Translations and sections@Translations and sections|indexit}{20}
\indexentry {LeftTranslation@`LeftTranslation'}{20}
\indexentry {RightTranslation@`RightTranslation'}{20}
\indexentry {LeftSection@`LeftSection'}{20}
\indexentry {RightSection@`RightSection'}{20}
\indexentry {Multiplication groups@Multiplication groups|indexit}{21}
\indexentry {LeftMultiplicationGroup@`LeftMultiplicationGroup'}{21}
\indexentry {RightMultiplicationGroup@`RightMultiplicationGroup'}{21}
\indexentry {MultiplicationGroup@`MultiplicationGroup'}{21}
\indexentry {multiplication group!relative left}{21}
\indexentry {multiplication group!relative right}{21}
\indexentry {multiplication group!relative}{21}
\indexentry {RelativeLeftMultiplicationGroup@`RelativeLeftMultiplicationGroup'}{21}
\indexentry {RelativeRightMultiplicationGroup@`RelativeRightMultiplicationGroup'}{21}
\indexentry {RelativeMultiplicationGroup@`RelativeMultiplicationGroup'}{21}
\indexentry {Inner mapping groups@Inner mapping groups|indexit}{21}
\indexentry {inner mapping group}{21}
\indexentry {inner mapping group!left}{21}
\indexentry {inner mapping group!right}{21}
\indexentry {inner mapping!left}{21}
\indexentry {inner mapping!right}{21}
\indexentry {conjugation}{21}
\indexentry {inner mapping!middle}{21}
\indexentry {inner mapping group!middle}{21}
\indexentry {LeftInnerMapping@`LeftInnerMapping'}{21}
\indexentry {MiddleInnerMapping@`MiddleInnerMapping'}{21}
\indexentry {RightInnerMapping@`RightInnerMapping'}{21}
\indexentry {LeftInnerMappingGroup@`LeftInnerMappingGroup'}{21}
\indexentry {MiddleInnerMappingGroup@`MiddleInnerMappingGroup'}{21}
\indexentry {RightInnerMappingGroup@`RightInnerMappingGroup'}{21}
\indexentry {InnerMappingGroup@`InnerMappingGroup'}{21}
\indexentry {Nuclei, commutant, center, and associator subloop@Nuclei, commutant, center, and associator subloop|indexit}{22}
\indexentry {nucleus!left}{22}
\indexentry {nucleus!middle}{22}
\indexentry {nucleus!right}{22}
\indexentry {nucleus}{22}
\indexentry {LeftNucleus@`LeftNucleus'}{22}
\indexentry {MiddleNucleus@`MiddleNucleus'}{22}
\indexentry {RightNucleus@`RightNucleus'}{22}
\indexentry {Nuc@`Nuc'}{22}
\indexentry {NucleusOfLoop@`NucleusOfLoop'}{22}
\indexentry {NucleusOfQuasigroup@`NucleusOfQuasigroup'}{22}
\indexentry {commutant}{22}
\indexentry {Commutant@`Commutant'}{22}
\indexentry {Center@`Center'}{22}
\indexentry {associator!subloop}{22}
\indexentry {subloop!associator}{22}
\indexentry {AssociatorSubloop@`AssociatorSubloop'}{22}
\indexentry {Normal subloops@Normal subloops|indexit}{22}
\indexentry {normal!subloop}{22}
\indexentry {subloop!normal}{22}
\indexentry {IsNormal@`IsNormal'}{22}
\indexentry {normal!closure}{22}
\indexentry {NormalClosure@`NormalClosure'}{22}
\indexentry {simple loop}{22}
\indexentry {loop!simple}{22}
\indexentry {IsSimple@`IsSimple'}{23}
\indexentry {Factor loops@Factor loops|indexit}{23}
\indexentry {FactorLoop@`FactorLoop'}{23}
\indexentry {NaturalHomomorphismByNormalSubloop@`NaturalHomomorphismByNormalSubloop'}{23}
\indexentry {Nilpotency and central series@Nilpotency and central series|indexit}{23}
\indexentry {NilpotencyClassOfLoop@`NilpotencyClassOfLoop'}{23}
\indexentry {IsNilpotent@`IsNilpotent'}{23}
\indexentry {strongly nilpotent loop}{23}
\indexentry {nilpotent loop!strongly}{23}
\indexentry {loop!strongly nilpotent}{23}
\indexentry {IsStronglyNilpotent@`IsStronglyNilpotent'}{23}
\indexentry {center!iterated}{23}
\indexentry {central series!upper}{23}
\indexentry {UpperCentralSeries@`UpperCentralSeries'}{23}
\indexentry {central series!lower}{23}
\indexentry {LowerCentralSeries@`LowerCentralSeries'}{23}
\indexentry {Solvability@Solvability|indexit}{23}
\indexentry {IsSolvable@`IsSolvable'}{23}
\indexentry {DerivedSubloop@`DerivedSubloop'}{23}
\indexentry {DerivedLength@`DerivedLength'}{23}
\indexentry {FrattiniSubloop@`FrattiniSubloop'}{23}
\indexentry {FrattinifactorSize@`FrattinifactorSize'}{23}
\indexentry {Isomorphisms and automorphisms@Isomorphisms and automorphisms|indexit}{23}
\indexentry {IsomorphismLoops@`IsomorphismLoops'}{24}
\indexentry {LoopsUpToIsomorphism@`LoopsUpToIsomorphism'}{24}
\indexentry {AutomorphismGroup@`AutomorphismGroup'}{24}
\indexentry {IsomorphicCopyByPerm@`IsomorphicCopyByPerm'}{24}
\indexentry {IsomorphicCopyByNormalSubloop@`IsomorphicCopyByNormalSubloop'}{24}
\indexentry {How are isomorphisms computed@How are isomorphisms computed|indexit}{24}
\indexentry {Discriminator@`Discriminator'}{24}
\indexentry {AreEqualDiscriminators@`AreEqualDiscriminators'}{24}
\indexentry {Isotopisms@Isotopisms|indexit}{24}
\indexentry {IsotopismLoops@`IsotopismLoops'}{24}
\indexentry {LoopsUpToIsotopism@`LoopsUpToIsotopism'}{25}
\indexentry {Associativity, commutativity and generalizations@Associativity, commutativity and generalizations|indexit}{26}
\indexentry {IsAssociative@`IsAssociative'}{26}
\indexentry {IsCommutative@`IsCommutative'}{26}
\indexentry {power associative!loop}{26}
\indexentry {loop!power associative}{26}
\indexentry {diassociative loop}{26}
\indexentry {loop!diassociative}{26}
\indexentry {IsPowerAssociative@`IsPowerAssociative'}{26}
\indexentry {IsDiassociative@`IsDiassociative'}{26}
\indexentry {Inverse properties@Inverse properties|indexit}{26}
\indexentry {inverse property!left}{26}
\indexentry {inverse property!right}{26}
\indexentry {inverse property}{26}
\indexentry {inverse!two-sided}{26}
\indexentry {HasLeftInverseProperty@`HasLeftInverseProperty'}{26}
\indexentry {HasRightInverseProperty@`HasRightInverseProperty'}{26}
\indexentry {HasInverseProperty@`HasInverseProperty'}{26}
\indexentry {HasTwosidedInverses@`HasTwosidedInverses'}{26}
\indexentry {inverse property!weak}{26}
\indexentry {HasWeakInverseProperty@`HasWeakInverseProperty'}{26}
\indexentry {inverse property!automorphic}{26}
\indexentry {inverse property!antiautomorphic}{26}
\indexentry {HasAutomorphicInverseProperty@`HasAutomorphicInverseProperty'}{26}
\indexentry {HasAntiautomorphicInverseProperty@`HasAntiautomorphicInverseProperty'}{26}
\indexentry {Some properties of quasigroups@Some properties of quasigroups|indexit}{26}
\indexentry {semisymmetric quasigroup}{26}
\indexentry {quasigroup!semisymmetric}{26}
\indexentry {totally symmetric quasigroup}{26}
\indexentry {quasigroup!totally symmetric}{26}
\indexentry {IsSemisymmetric@`IsSemisymmetric'}{27}
\indexentry {IsTotallySymmetric@`IsTotallySymmetric'}{27}
\indexentry {idempotent quasigroup}{27}
\indexentry {quasigroup!idempotent}{27}
\indexentry {Steiner!quasigroup}{27}
\indexentry {quasigroup!Steiner}{27}
\indexentry {unipotent quasigroup}{27}
\indexentry {quasigroup!unipotent}{27}
\indexentry {IsIdempotent@`IsIdempotent'}{27}
\indexentry {IsSteinerQuasigroup@`IsSteinerQuasigroup'}{27}
\indexentry {IsUnipotent@`IsUnipotent'}{27}
\indexentry {distributive quasigroup!left}{27}
\indexentry {distributive quasigroup!right}{27}
\indexentry {distributive quasigroup}{27}
\indexentry {quasigroup!distributive}{27}
\indexentry {entropic quasigroup}{27}
\indexentry {quasigroup!entropic}{27}
\indexentry {medial quasigroup}{27}
\indexentry {quasigroup!medial}{27}
\indexentry {IsLeftDistributive@`IsLeftDistributive'}{27}
\indexentry {IsRightDistributive@`IsRightDistributive'}{27}
\indexentry {IsDistributive@`IsDistributive'}{27}
\indexentry {IsEntropic@`IsEntropic'}{27}
\indexentry {IsMedial@`IsMedial'}{27}
\indexentry {IsLDistributive@`IsLDistributive'}{27}
\indexentry {IsRDistributive@`IsRDistributive'}{27}
\indexentry {Loops of Bol-Moufang type@Loops of Bol-Moufang type|indexit}{27}
\indexentry {loop!of Bol-Moufang type}{27}
\indexentry {identity of Bol-Moufang type}{27}
\indexentry {alternative loop!left}{27}
\indexentry {alternative loop!right}{27}
\indexentry {nuclear square loop!left}{27}
\indexentry {nuclear square loop!middle}{27}
\indexentry {nuclear square loop!right}{27}
\indexentry {flexible loop}{27}
\indexentry {loop!flexible}{27}
\indexentry {Bol loop!left}{27}
\indexentry {loop!Bol}{27}
\indexentry {Bol loop!right}{27}
\indexentry {LC-loop}{27}
\indexentry {loop!LC}{27}
\indexentry {RC-loop}{27}
\indexentry {loop!RC}{27}
\indexentry {Moufang loop}{27}
\indexentry {loop!Moufang}{27}
\indexentry {C-loop}{27}
\indexentry {loop!C}{27}
\indexentry {extra loop}{27}
\indexentry {loop!extra}{27}
\indexentry {alternative loop}{27}
\indexentry {loop!alternative}{27}
\indexentry {nuclear square loop}{27}
\indexentry {loop!nuclear square}{27}
\indexentry {IsExtraLoop@`IsExtraLoop'}{28}
\indexentry {IsMoufangLoop@`IsMoufangLoop'}{28}
\indexentry {IsCLoop@`IsCLoop'}{28}
\indexentry {IsLeftBolLoop@`IsLeftBolLoop'}{28}
\indexentry {IsRightBolLoop@`IsRightBolLoop'}{28}
\indexentry {IsLCLoop@`IsLCLoop'}{28}
\indexentry {IsRCLoop@`IsRCLoop'}{28}
\indexentry {IsLeftNuclearSquareLoop@`IsLeftNuclearSquareLoop'}{28}
\indexentry {IsMiddleNuclearSquareLoop@`IsMiddleNuclearSquareLoop'}{28}
\indexentry {IsRightNuclearSquareLoop@`IsRightNuclearSquareLoop'}{28}
\indexentry {IsNuclearSquareLoop@`IsNuclearSquareLoop'}{28}
\indexentry {IsFlexible@`IsFlexible'}{28}
\indexentry {IsLeftAlternative@`IsLeftAlternative'}{28}
\indexentry {IsRightAlternative@`IsRightAlternative'}{28}
\indexentry {IsAlternative@`IsAlternative'}{28}
\indexentry {Power alternative loops@Power alternative loops|indexit}{28}
\indexentry {power alternative loop!left}{28}
\indexentry {power alternative loop!right}{28}
\indexentry {power alternative loop}{28}
\indexentry {loop!power alternative}{28}
\indexentry {IsLeftPowerAlternative@`IsLeftPowerAlternative'}{28}
\indexentry {IsRightPowerAlternative@`IsRightPowerAlternative'}{28}
\indexentry {IsPowerAlternative@`IsPowerAlternative'}{28}
\indexentry {Conjugacy closed loops and related properties@Conjugacy closed loops and related properties|indexit}{28}
\indexentry {conjugacy closed loop!left}{28}
\indexentry {conjugacy closed loop!right}{28}
\indexentry {conjugacy closed loop}{28}
\indexentry {loop!conjugacy closed}{28}
\indexentry {IsLCCLoop@`IsLCCLoop'}{28}
\indexentry {IsRCCLoop@`IsRCCLoop'}{28}
\indexentry {IsCCLoop@`IsCCLoop'}{28}
\indexentry {Osborn loop}{29}
\indexentry {loop!Osborn}{29}
\indexentry {IsOsbornLoop@`IsOsbornLoop'}{29}
\indexentry {Additional varieties of loops@Additional varieties of loops|indexit}{29}
\indexentry {code loop}{29}
\indexentry {loop!code}{29}
\indexentry {IsCodeLoop@`IsCodeLoop'}{29}
\indexentry {Steiner!loop}{29}
\indexentry {loop!Steiner}{29}
\indexentry {IsSteinerLoop@`IsSteinerLoop'}{29}
\indexentry {Bruck loop!left}{29}
\indexentry {Bruck loop!right}{29}
\indexentry {Bruck loop}{29}
\indexentry {loop!Bruck}{29}
\indexentry {K-loop}{29}
\indexentry {loop!K}{29}
\indexentry {IsLeftBruckLoop@`IsLeftBruckLoop'}{29}
\indexentry {IsLeftKLoop@`IsLeftKLoop'}{29}
\indexentry {IsRightBruckLoop@`IsRightBruckLoop'}{29}
\indexentry {IsRightKLoop@`IsRightKLoop'}{29}
\indexentry {automorphic loop!left}{29}
\indexentry {automorphic loop!middle}{29}
\indexentry {automorphic loop!right}{29}
\indexentry {automorphic loop}{29}
\indexentry {loop!automorphic}{29}
\indexentry {IsLeftAutomorphicLoop@`IsLeftAutomorphicLoop'}{29}
\indexentry {IsMiddleAutomorphicLoop@`IsMiddleAutomorphicLoop'}{29}
\indexentry {IsRightAutomorphicLoop@`IsRightAutomorphicLoop'}{29}
\indexentry {IsAutomorphicLoop@`IsAutomorphicLoop'}{29}
\indexentry {A-loop}{29}
\indexentry {loop!A}{29}
\indexentry {IsLeftALoop@`IsLeftALoop'}{29}
\indexentry {IsMiddleALoop@`IsMiddleALoop'}{29}
\indexentry {IsRightALoop@`IsRightALoop'}{29}
\indexentry {IsALoop@`IsALoop'}{29}
\indexentry {Core methods for Bol loops@Core methods for Bol loops|indexit}{30}
\indexentry {Bol loop!left}{30}
\indexentry {loop!Bol}{30}
\indexentry {Bruck loop!associated left}{30}
\indexentry {loop!associated Bruck}{30}
\indexentry {AssociatedLeftBruckLoop@`AssociatedLeftBruckLoop'}{30}
\indexentry {Moufang modifications@Moufang modifications|indexit}{30}
\indexentry {modification!Moufang}{30}
\indexentry {modification!cyclic}{30}
\indexentry {LoopByCyclicModification@`LoopByCyclicModification'}{30}
\indexentry {modification!dihedral}{30}
\indexentry {LoopByDihedralModification@`LoopByDihedralModification'}{30}
\indexentry {LoopMG2@`LoopMG2'}{30}
\indexentry {Triality for Moufang loops@Triality for Moufang loops|indexit}{30}
\indexentry {group with triality}{30}
\indexentry {TrialityPermGroup@`TrialityPermGroup'}{31}
\indexentry {TrialityPcGroup@`TrialityPcGroup'}{31}
\indexentry {Realizing groups as multiplication groups of loops@Realizing groups as multiplication groups of loops|indexit}{31}
\indexentry {AllLoopTablesInGroup@`AllLoopTablesInGroup'}{31}
\indexentry {AllProperLoopTablesInGroup@`AllProperLoopTablesInGroup'}{31}
\indexentry {OneLoopTableInGroup@`OneLoopTableInGroup'}{31}
\indexentry {OneProperLoopTableInGroup@`OneProperLoopTableInGroup'}{31}
\indexentry {AllLoopsWithMltGroup@`AllLoopsWithMltGroup'}{31}
\indexentry {OneLoopWithMltGroup@`OneLoopWithMltGroup'}{31}
\indexentry {A typical library@A typical library|indexit}{32}
\indexentry {MyLibraryLoop@`MyLibraryLoop'}{32}
\indexentry {LibraryLoop@`LibraryLoop'}{32}
\indexentry {DisplayLibraryInfo@`DisplayLibraryInfo'}{32}
\indexentry {Left Bol loops@Left Bol loops|indexit}{32}
\indexentry {LeftBolLoop@`LeftBolLoop'}{32}
\indexentry {Moufang loops@Moufang loops|indexit}{32}
\indexentry {MoufangLoop@`MoufangLoop'}{32}
\indexentry {octonion loop}{33}
\indexentry {loop!octonion}{33}
\indexentry {Code loops@Code loops|indexit}{33}
\indexentry {CodeLoop@`CodeLoop'}{33}
\indexentry {Steiner loops@Steiner loops|indexit}{33}
\indexentry {SteinerLoop@`SteinerLoop'}{33}
\indexentry {CC-loops@CC-loops|indexit}{33}
\indexentry {conjugacy closed loop}{33}
\indexentry {loop!conjugacy closed}{33}
\indexentry {CCLoop@`CCLoop'}{34}
\indexentry {Small loops@Small loops|indexit}{34}
\indexentry {SmallLoop@`SmallLoop'}{34}
\indexentry {Paige loops@Paige loops|indexit}{34}
\indexentry {Paige loop}{34}
\indexentry {loop!Paige}{34}
\indexentry {PaigeLoop@`PaigeLoop'}{34}
\indexentry {Nilpotent loops@Nilpotent loops|indexit}{34}
\indexentry {NilpotentLoop@`NilpotentLoop'}{34}
\indexentry {Automorphic loops@Automorphic loops|indexit}{34}
\indexentry {AutomorphicLoop@`AutomorphicLoop'}{34}
\indexentry {Interesting loops@Interesting loops|indexit}{34}
\indexentry {sedenion loop}{34}
\indexentry {loop!sedenion}{34}
\indexentry {InterestingLoop@`InterestingLoop'}{34}
\indexentry {Libraries of loops up to isotopism@Libraries of loops up to isotopism|indexit}{34}
\indexentry {ItpSmallLoop@`ItpSmallLoop'}{35}
