\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 {two-sided inverse}{6}
\indexentry {group}{6}
\indexentry {quasigroup}{6}
\indexentry {Latin square}{6}
\indexentry {loop}{6}
\indexentry {Translations@Translations|indexit}{6}
\indexentry {left translation}{6}
\indexentry {right translation}{6}
\indexentry {left section}{6}
\indexentry {right section}{6}
\indexentry {left multiplication group}{6}
\indexentry {right multiplication group}{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 {principal isotopism}{6}
\indexentry {principal loop isotope}{6}
\indexentry {Extensions@Extensions|indexit}{6}
\indexentry {extension of loops}{6}
\indexentry {nuclear extension}{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 {AsLoop@`AsLoop'}{8}
\indexentry {AsQuasigroup@`AsQuasigroup'}{8}
\indexentry {AsLoop@`AsLoop'}{8}
\indexentry {Calculating with quasigroups@Calculating with quasigroups|indexit}{9}
\indexentry {Bol loop}{9}
\indexentry {simple loop}{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 {Cayley table}{11}
\indexentry {multiplication table}{11}
\indexentry {quasigroup table}{11}
\indexentry {Latin square}{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 {simple Bol loop}{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 {Conversions@Conversions|indexit}{14}
\indexentry {AsQuasigroup@`AsQuasigroup'}{14}
\indexentry {PrincipalLoopIsotope@`PrincipalLoopIsotope'}{14}
\indexentry {AsLoop@`AsLoop'}{14}
\indexentry {AsGroup@`AsGroup'}{15}
\indexentry {Products of loops@Products of loops|indexit}{15}
\indexentry {DirectProduct@`DirectProduct'}{15}
\indexentry {Opposite quasigroups and loops@Opposite quasigroups and loops|indexit}{15}
\indexentry {opposite quasigroup}{15}
\indexentry {Opposite@`Opposite'}{15}
\indexentry {Basic attributes@Basic attributes|indexit}{16}
\indexentry {Elements@`Elements'}{16}
\indexentry {CayleyTable@`CayleyTable'}{16}
\indexentry {One@`One'}{16}
\indexentry {MultiplicativeNeutralElement@`MultiplicativeNeutralElement'}{16}
\indexentry {Size@`Size'}{16}
\indexentry {power-associative loop}{16}
\indexentry {exponent}{16}
\indexentry {Exponent@`Exponent'}{16}
\indexentry {Basic arithmetic operations@Basic arithmetic operations|indexit}{16}
\indexentry {left division}{16}
\indexentry {right division}{16}
\indexentry {LeftDivision@`LeftDivision'}{16}
\indexentry {RightDivision@`RightDivision'}{16}
\indexentry {LeftDivision@`LeftDivision'}{16}
\indexentry {LeftDivision@`LeftDivision'}{16}
\indexentry {RightDivision@`RightDivision'}{16}
\indexentry {RightDivision@`RightDivision'}{16}
\indexentry {LeftDivisionCayleyTable@`LeftDivisionCayleyTable'}{17}
\indexentry {RightDivisionCayleyTable@`RightDivisionCayleyTable'}{17}
\indexentry {Powers and inverses@Powers and inverses|indexit}{17}
\indexentry {power-associativity}{17}
\indexentry {left inverse}{17}
\indexentry {right inverse}{17}
\indexentry {inverse}{17}
\indexentry {LeftInverse@`LeftInverse'}{17}
\indexentry {RightInverse@`RightInverse'}{17}
\indexentry {Inverse@`Inverse'}{17}
\indexentry {Associators and commutators@Associators and commutators|indexit}{17}
\indexentry {associator}{17}
\indexentry {commutator}{17}
\indexentry {Associator@`Associator'}{17}
\indexentry {Commutator@`Commutator'}{17}
\indexentry {Generators@Generators|indexit}{17}
\indexentry {GeneratorsOfQuasigroup@`GeneratorsOfQuasigroup'}{17}
\indexentry {GeneratorsOfLoop@`GeneratorsOfLoop'}{17}
\indexentry {GeneratorsSmallest@`GeneratorsSmallest'}{17}
\indexentry {Parent of a quasigroup@Parent of a quasigroup|indexit}{18}
\indexentry {Parent@`Parent'}{18}
\indexentry {Position@`Position'}{18}
\indexentry {PosInParent@`PosInParent'}{18}
\indexentry {Comparing quasigroups with common parent@Comparing quasigroups with common parent|indexit}{18}
\indexentry {Subquasigroups and subloops@Subquasigroups and subloops|indexit}{18}
\indexentry {Subquasigroup@`Subquasigroup'}{18}
\indexentry {Subloop@`Subloop'}{18}
\indexentry {IsSubquasigroup@`IsSubquasigroup'}{19}
\indexentry {IsSubloop@`IsSubloop'}{19}
\indexentry {AllSubloops@`AllSubloops'}{19}
\indexentry {coset}{19}
\indexentry {RightCosets@`RightCosets'}{19}
\indexentry {transversal}{19}
\indexentry {RightTransversal@`RightTransversal'}{19}
\indexentry {Translations and sections@Translations and sections|indexit}{19}
\indexentry {LeftTranslation@`LeftTranslation'}{19}
\indexentry {RightTranslation@`RightTranslation'}{19}
\indexentry {LeftSection@`LeftSection'}{19}
\indexentry {RightSection@`RightSection'}{19}
\indexentry {Multiplication groups@Multiplication groups|indexit}{20}
\indexentry {LeftMultiplicationGroup@`LeftMultiplicationGroup'}{20}
\indexentry {RightMultiplicationGroup@`RightMultiplicationGroup'}{20}
\indexentry {MultiplicationGroup@`MultiplicationGroup'}{20}
\indexentry {relative left multiplication group}{20}
\indexentry {relative right multiplication group}{20}
\indexentry {relative multiplication group}{20}
\indexentry {RelativeLeftMultiplicationGroup@`RelativeLeftMultiplicationGroup'}{20}
\indexentry {RelativeRightMultiplicationGroup@`RelativeRightMultiplicationGroup'}{20}
\indexentry {RelativeMultiplicationGroup@`RelativeMultiplicationGroup'}{20}
\indexentry {Inner mapping groups@Inner mapping groups|indexit}{20}
\indexentry {inner mapping group}{20}
\indexentry {left inner mapping group}{20}
\indexentry {right inner mapping group}{20}
\indexentry {left inner mapping}{20}
\indexentry {right inner mapping}{20}
\indexentry {conjugation}{20}
\indexentry {middle inner mapping}{20}
\indexentry {middle inner mapping}{20}
\indexentry {LeftInnerMapping@`LeftInnerMapping'}{20}
\indexentry {MiddleInnerMapping@`MiddleInnerMapping'}{20}
\indexentry {RightInnerMapping@`RightInnerMapping'}{20}
\indexentry {LeftInnerMappingGroup@`LeftInnerMappingGroup'}{20}
\indexentry {MiddleInnerMappingGroup@`MiddleInnerMappingGroup'}{20}
\indexentry {RightInnerMappingGroup@`RightInnerMappingGroup'}{20}
\indexentry {InnerMappingGroup@`InnerMappingGroup'}{20}
\indexentry {Nuclei, commutant, center, and associator subloop@Nuclei, commutant, center, and associator subloop|indexit}{21}
\indexentry {left nucleus}{21}
\indexentry {middle nucleus}{21}
\indexentry {right nucleus}{21}
\indexentry {nucleus}{21}
\indexentry {LeftNucleus@`LeftNucleus'}{21}
\indexentry {MiddleNucleus@`MiddleNucleus'}{21}
\indexentry {RightNucleus@`RightNucleus'}{21}
\indexentry {Nuc@`Nuc'}{21}
\indexentry {NucleusOfLoop@`NucleusOfLoop'}{21}
\indexentry {NucleusOfQuasigroup@`NucleusOfQuasigroup'}{21}
\indexentry {commutant}{21}
\indexentry {Moufang center}{21}
\indexentry {centrum}{21}
\indexentry {Commutant@`Commutant'}{21}
\indexentry {Center@`Center'}{21}
\indexentry {associator subloop}{21}
\indexentry {AssociatorSubloop@`AssociatorSubloop'}{21}
\indexentry {Normal subloops@Normal subloops|indexit}{21}
\indexentry {normal subloop}{21}
\indexentry {IsNormal@`IsNormal'}{21}
\indexentry {normal closure}{21}
\indexentry {NormalClosure@`NormalClosure'}{21}
\indexentry {simple loop}{21}
\indexentry {IsSimple@`IsSimple'}{21}
\indexentry {Factor loops@Factor loops|indexit}{21}
\indexentry {FactorLoop@`FactorLoop'}{21}
\indexentry {NaturalHomomorphismByNormalSubloop@`NaturalHomomorphismByNormalSubloop'}{22}
\indexentry {Nilpotency and central series@Nilpotency and central series|indexit}{22}
\indexentry {NilpotencyClassOfLoop@`NilpotencyClassOfLoop'}{22}
\indexentry {IsNilpotent@`IsNilpotent'}{22}
\indexentry {strongly nilpotent loop}{22}
\indexentry {IsStronglyNilpotent@`IsStronglyNilpotent'}{22}
\indexentry {iterated centers}{22}
\indexentry {upper central series}{22}
\indexentry {UpperCentralSeries@`UpperCentralSeries'}{22}
\indexentry {lower central series}{22}
\indexentry {LowerCentralSeries@`LowerCentralSeries'}{22}
\indexentry {Solvability@Solvability|indexit}{22}
\indexentry {IsSolvable@`IsSolvable'}{22}
\indexentry {DerivedSubloop@`DerivedSubloop'}{22}
\indexentry {DerivedLength@`DerivedLength'}{22}
\indexentry {FrattiniSubloop@`FrattiniSubloop'}{22}
\indexentry {FrattinifactorSize@`FrattinifactorSize'}{22}
\indexentry {Isomorphisms and automorphisms@Isomorphisms and automorphisms|indexit}{22}
\indexentry {IsomorphismLoops@`IsomorphismLoops'}{22}
\indexentry {LoopsUpToIsomorphism@`LoopsUpToIsomorphism'}{22}
\indexentry {AutomorphismGroup@`AutomorphismGroup'}{23}
\indexentry {IsomorphicCopyByPerm@`IsomorphicCopyByPerm'}{23}
\indexentry {IsomorphicCopyByNormalSubloop@`IsomorphicCopyByNormalSubloop'}{23}
\indexentry {How are isomorphisms computed@How are isomorphisms computed|indexit}{23}
\indexentry {Discriminator@`Discriminator'}{23}
\indexentry {AreEqualDiscriminators@`AreEqualDiscriminators'}{23}
\indexentry {Isotopisms@Isotopisms|indexit}{23}
\indexentry {IsotopismLoops@`IsotopismLoops'}{23}
\indexentry {LoopsUpToIsotopism@`LoopsUpToIsotopism'}{23}
\indexentry {Associativity, commutativity and generalizations@Associativity, commutativity and generalizations|indexit}{25}
\indexentry {IsAssociative@`IsAssociative'}{25}
\indexentry {IsCommutative@`IsCommutative'}{25}
\indexentry {power-associative loop}{25}
\indexentry {diassociative loop}{25}
\indexentry {IsPowerAssociative@`IsPowerAssociative'}{25}
\indexentry {IsDiassociative@`IsDiassociative'}{25}
\indexentry {Inverse properties@Inverse properties|indexit}{25}
\indexentry {left inverse property}{25}
\indexentry {right inverse property}{25}
\indexentry {inverse property}{25}
\indexentry {two-sided inverses loop}{25}
\indexentry {HasLeftInverseProperty@`HasLeftInverseProperty'}{25}
\indexentry {HasRightInverseProperty@`HasRightInverseProperty'}{25}
\indexentry {HasInverseProperty@`HasInverseProperty'}{25}
\indexentry {HasTwosidedInverses@`HasTwosidedInverses'}{25}
\indexentry {weak inverse property}{25}
\indexentry {HasWeakInverseProperty@`HasWeakInverseProperty'}{25}
\indexentry {automorphic inverse property}{25}
\indexentry {antiautomorphic inverse property}{25}
\indexentry {HasAutomorphicInverseProperty@`HasAutomorphicInverseProperty'}{25}
\indexentry {HasAntiautomorphicInverseProperty@`HasAntiautomorphicInverseProperty'}{25}
\indexentry {Some properties of quasigroups@Some properties of quasigroups|indexit}{25}
\indexentry {semisymmetric quasigroup}{25}
\indexentry {totally symmetric quasigroup}{25}
\indexentry {IsSemisymmetric@`IsSemisymmetric'}{26}
\indexentry {IsTotallySymmetric@`IsTotallySymmetric'}{26}
\indexentry {idempotent quasigroup}{26}
\indexentry {Steiner quasigroup}{26}
\indexentry {unipotent quasigroup}{26}
\indexentry {IsIdempotent@`IsIdempotent'}{26}
\indexentry {IsSteinerQuasigroup@`IsSteinerQuasigroup'}{26}
\indexentry {IsUnipotent@`IsUnipotent'}{26}
\indexentry {left distributive quasigroup}{26}
\indexentry {right distributive quasigroup}{26}
\indexentry {distributive quasigroup}{26}
\indexentry {entropic quasigroup}{26}
\indexentry {medial quasigroup}{26}
\indexentry {IsLeftDistributive@`IsLeftDistributive'}{26}
\indexentry {IsRightDistributive@`IsRightDistributive'}{26}
\indexentry {IsDistributive@`IsDistributive'}{26}
\indexentry {IsEntropic@`IsEntropic'}{26}
\indexentry {IsMedial@`IsMedial'}{26}
\indexentry {IsLDistributive@`IsLDistributive'}{26}
\indexentry {IsRDistributive@`IsRDistributive'}{26}
\indexentry {Loops of Bol-Moufang type@Loops of Bol-Moufang type|indexit}{26}
\indexentry {loops of Bol-Moufang type}{26}
\indexentry {identity of Bol-Moufang type}{26}
\indexentry {left alternative loop}{26}
\indexentry {right alternative loop}{26}
\indexentry {left nuclear square loop}{26}
\indexentry {middle nuclear square loop}{26}
\indexentry {right nuclear square loop}{26}
\indexentry {flexible loop}{26}
\indexentry {left Bol loop}{26}
\indexentry {right Bol loop}{26}
\indexentry {LC-loop}{26}
\indexentry {RC-loop}{26}
\indexentry {Moufang loop}{26}
\indexentry {C-loop}{26}
\indexentry {extra loop}{26}
\indexentry {alternative loop}{26}
\indexentry {nuclear square loop}{26}
\indexentry {IsExtraLoop@`IsExtraLoop'}{27}
\indexentry {IsMoufangLoop@`IsMoufangLoop'}{27}
\indexentry {IsCLoop@`IsCLoop'}{27}
\indexentry {IsLeftBolLoop@`IsLeftBolLoop'}{27}
\indexentry {IsRightBolLoop@`IsRightBolLoop'}{27}
\indexentry {IsLCLoop@`IsLCLoop'}{27}
\indexentry {IsRCLoop@`IsRCLoop'}{27}
\indexentry {IsLeftNuclearSquareLoop@`IsLeftNuclearSquareLoop'}{27}
\indexentry {IsMiddleNuclearSquareLoop@`IsMiddleNuclearSquareLoop'}{27}
\indexentry {IsRightNuclearSquareLoop@`IsRightNuclearSquareLoop'}{27}
\indexentry {IsNuclearSquareLoop@`IsNuclearSquareLoop'}{27}
\indexentry {IsFlexible@`IsFlexible'}{27}
\indexentry {IsLeftAlternative@`IsLeftAlternative'}{27}
\indexentry {IsRightAlternative@`IsRightAlternative'}{27}
\indexentry {IsAlternative@`IsAlternative'}{27}
\indexentry {Power alternative loops@Power alternative loops|indexit}{27}
\indexentry {left power alternative loop}{27}
\indexentry {right power alternative loop}{27}
\indexentry {power alternative loop}{27}
\indexentry {IsLeftPowerAlternative@`IsLeftPowerAlternative'}{27}
\indexentry {IsRightPowerAlternative@`IsRightPowerAlternative'}{27}
\indexentry {IsPowerAlternative@`IsPowerAlternative'}{27}
\indexentry {Conjugacy closed loops and related properties@Conjugacy closed loops and related properties|indexit}{27}
\indexentry {left conjugacy closed loop}{27}
\indexentry {right conjugacy closed loop}{27}
\indexentry {conjugacy closed loop}{27}
\indexentry {IsLCCLoop@`IsLCCLoop'}{27}
\indexentry {IsRCCLoop@`IsRCCLoop'}{27}
\indexentry {IsCCLoop@`IsCCLoop'}{27}
\indexentry {Osborn loop}{28}
\indexentry {IsOsbornLoop@`IsOsbornLoop'}{28}
\indexentry {Additional varieties of loops@Additional varieties of loops|indexit}{28}
\indexentry {code loop}{28}
\indexentry {IsCodeLoop@`IsCodeLoop'}{28}
\indexentry {Steiner loop}{28}
\indexentry {IsSteinerLoop@`IsSteinerLoop'}{28}
\indexentry {left Bruck loop}{28}
\indexentry {right Bruck loop}{28}
\indexentry {K-loop}{28}
\indexentry {IsLeftBruckLoop@`IsLeftBruckLoop'}{28}
\indexentry {IsLeftKLoop@`IsLeftKLoop'}{28}
\indexentry {IsRightBruckLoop@`IsRightBruckLoop'}{28}
\indexentry {IsRightKLoop@`IsRightKLoop'}{28}
\indexentry {left A-loop}{28}
\indexentry {middle A-loop}{28}
\indexentry {right A-loop}{28}
\indexentry {A-loop}{28}
\indexentry {IsLeftALoop@`IsLeftALoop'}{28}
\indexentry {IsMiddleALoop@`IsMiddleALoop'}{28}
\indexentry {IsRightALoop@`IsRightALoop'}{28}
\indexentry {IsALoop@`IsALoop'}{28}
\indexentry {Core methods for Bol loops@Core methods for Bol loops|indexit}{29}
\indexentry {left Bol loop}{29}
\indexentry {associated left Bruck loop}{29}
\indexentry {AssoicatedLeftBruckLoop@`AssoicatedLeftBruckLoop'}{29}
\indexentry {Moufang modifications@Moufang modifications|indexit}{29}
\indexentry {Moufang modifications}{29}
\indexentry {cyclic modification}{29}
\indexentry {LoopByCyclicModification@`LoopByCyclicModification'}{29}
\indexentry {dihedral modification}{29}
\indexentry {LoopByDihedralModification@`LoopByDihedralModification'}{29}
\indexentry {LoopMG2@`LoopMG2'}{29}
\indexentry {Triality for Moufang loops@Triality for Moufang loops|indexit}{29}
\indexentry {group with triality}{29}
\indexentry {TrialityPermGroup@`TrialityPermGroup'}{30}
\indexentry {TrialityPcGroup@`TrialityPcGroup'}{30}
\indexentry {A typical library@A typical library|indexit}{31}
\indexentry {MyLibraryLoop@`MyLibraryLoop'}{31}
\indexentry {LibraryLoop@`LibraryLoop'}{31}
\indexentry {DisplayLibraryInfo@`DisplayLibraryInfo'}{31}
\indexentry {Left Bol loops@Left Bol loops|indexit}{31}
\indexentry {LeftBolLoop@`LeftBolLoop'}{31}
\indexentry {Moufang loops@Moufang loops|indexit}{31}
\indexentry {MoufangLoop@`MoufangLoop'}{31}
\indexentry {octonion loop}{32}
\indexentry {octonions}{32}
\indexentry {Code loops@Code loops|indexit}{32}
\indexentry {CodeLoop@`CodeLoop'}{32}
\indexentry {Steiner loops@Steiner loops|indexit}{32}
\indexentry {SteinerLoop@`SteinerLoop'}{32}
\indexentry {CC-loops@CC-loops|indexit}{32}
\indexentry {conjugacy closed loop}{32}
\indexentry {CCLoop@`CCLoop'}{33}
\indexentry {Small loops@Small loops|indexit}{33}
\indexentry {SmallLoop@`SmallLoop'}{33}
\indexentry {Paige loops@Paige loops|indexit}{33}
\indexentry {Paige loop}{33}
\indexentry {PaigeLoop@`PaigeLoop'}{33}
\indexentry {Interesting loops@Interesting loops|indexit}{33}
\indexentry {sedenions}{33}
\indexentry {InterestingLoop@`InterestingLoop'}{33}
\indexentry {Libraries of loops up to isotopism@Libraries of loops up to isotopism|indexit}{33}
\indexentry {ItpSmallLoop@`ItpSmallLoop'}{33}
\indexentry {list of files}{35}