\indexentry {Installation@Installation|indexit}{5}
\indexentry {Documentation@Documentation|indexit}{5}
\indexentry {Test files@Test files|indexit}{5}
\indexentry {Feedback@Feedback|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 {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 {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 {Conversions@Conversions|indexit}{12}
\indexentry {AsQuasigroup@`AsQuasigroup'}{12}
\indexentry {AsLoop@`AsLoop'}{12}
\indexentry {PrincipalLoopIsotope@`PrincipalLoopIsotope'}{13}
\indexentry {AsGroup@`AsGroup'}{13}
\indexentry {Products of loops@Products of loops|indexit}{13}
\indexentry {DirectProduct@`DirectProduct'}{13}
\indexentry {Opposite quasigroups and loops@Opposite quasigroups and loops|indexit}{13}
\indexentry {opposite quasigroup}{13}
\indexentry {Opposite@`Opposite'}{13}
\indexentry {Basic attributes@Basic attributes|indexit}{13}
\indexentry {Elements@`Elements'}{13}
\indexentry {CayleyTable@`CayleyTable'}{13}
\indexentry {One@`One'}{13}
\indexentry {MultiplicativeNeutralElement@`MultiplicativeNeutralElement'}{13}
\indexentry {Size@`Size'}{14}
\indexentry {power-associative loop}{14}
\indexentry {exponent}{14}
\indexentry {Exponent@`Exponent'}{14}
\indexentry {Basic arithmetic operations@Basic arithmetic operations|indexit}{14}
\indexentry {left division}{14}
\indexentry {right division}{14}
\indexentry {LeftDivision@`LeftDivision'}{14}
\indexentry {RightDivision@`RightDivision'}{14}
\indexentry {LeftDivision@`LeftDivision'}{14}
\indexentry {LeftDivision@`LeftDivision'}{14}
\indexentry {RightDivision@`RightDivision'}{14}
\indexentry {RightDivision@`RightDivision'}{14}
\indexentry {LeftDivisionCayleyTable@`LeftDivisionCayleyTable'}{15}
\indexentry {RightDivisionCayleyTable@`RightDivisionCayleyTable'}{15}
\indexentry {Powers and inverses@Powers and inverses|indexit}{15}
\indexentry {power-associative}{15}
\indexentry {left inverse}{15}
\indexentry {right inverse}{15}
\indexentry {inverse}{15}
\indexentry {LeftInverse@`LeftInverse'}{15}
\indexentry {RightInverse@`RightInverse'}{15}
\indexentry {Inverse@`Inverse'}{15}
\indexentry {Associators and commutators@Associators and commutators|indexit}{15}
\indexentry {associator}{15}
\indexentry {commutator}{15}
\indexentry {Associator@`Associator'}{15}
\indexentry {Commutator@`Commutator'}{15}
\indexentry {Generators@Generators|indexit}{15}
\indexentry {GeneratorsOfQuasigroup@`GeneratorsOfQuasigroup'}{15}
\indexentry {GeneratorsOfLoop@`GeneratorsOfLoop'}{15}
\indexentry {GeneratorsSmallest@`GeneratorsSmallest'}{15}
\indexentry {Parent of a quasigroup@Parent of a quasigroup|indexit}{17}
\indexentry {Parent@`Parent'}{17}
\indexentry {Position@`Position'}{17}
\indexentry {PosInParent@`PosInParent'}{17}
\indexentry {Comparing quasigroups with common parent@Comparing quasigroups with common parent|indexit}{17}
\indexentry {Subquasigroups and subloops@Subquasigroups and subloops|indexit}{17}
\indexentry {Subquasigroup@`Subquasigroup'}{17}
\indexentry {Subloop@`Subloop'}{17}
\indexentry {IsSubquasigroup@`IsSubquasigroup'}{17}
\indexentry {IsSubloop@`IsSubloop'}{17}
\indexentry {Translations and sections@Translations and sections|indexit}{18}
\indexentry {LeftTranslation@`LeftTranslation'}{18}
\indexentry {RightTranslation@`RightTranslation'}{18}
\indexentry {LeftSection@`LeftSection'}{18}
\indexentry {RightSection@`RightSection'}{18}
\indexentry {Multiplication groups@Multiplication groups|indexit}{18}
\indexentry {LeftMultiplicationGroup@`LeftMultiplicationGroup'}{18}
\indexentry {RightMultiplicationGroup@`RightMultiplicationGroup'}{18}
\indexentry {MultiplicationGroup@`MultiplicationGroup'}{18}
\indexentry {relative left multiplication group}{18}
\indexentry {relative right multiplication group}{18}
\indexentry {relative multiplication group}{18}
\indexentry {RelativeLeftMultiplicationGroup@`RelativeLeftMultiplicationGroup'}{19}
\indexentry {RelativeRightMultiplicationGroup@`RelativeRightMultiplicationGroup'}{19}
\indexentry {RelativeMultiplicationGroup@`RelativeMultiplicationGroup'}{19}
\indexentry {Inner mapping groups@Inner mapping groups|indexit}{19}
\indexentry {inner mapping group}{19}
\indexentry {left inner mapping group}{19}
\indexentry {right inner mapping group}{19}
\indexentry {InnerMappingGroup@`InnerMappingGroup'}{19}
\indexentry {LeftInnerMappingGroup@`LeftInnerMappingGroup'}{19}
\indexentry {RightInnerMappingGroup@`RightInnerMappingGroup'}{19}
\indexentry {Nuclei, commutant, center, and associator subloop@Nuclei, commutant, center, and associator subloop|indexit}{19}
\indexentry {left nucleus}{19}
\indexentry {middle nucleus}{19}
\indexentry {right nucleus}{19}
\indexentry {nucleus}{19}
\indexentry {LeftNucleus@`LeftNucleus'}{19}
\indexentry {MiddleNucleus@`MiddleNucleus'}{19}
\indexentry {RightNucleus@`RightNucleus'}{19}
\indexentry {Nuc@`Nuc'}{19}
\indexentry {NucleusOfLoop@`NucleusOfLoop'}{19}
\indexentry {NucleusOfQuasigroup@`NucleusOfQuasigroup'}{19}
\indexentry {commutant}{19}
\indexentry {Moufang center}{19}
\indexentry {Commutant@`Commutant'}{19}
\indexentry {Center@`Center'}{19}
\indexentry {associator subloop}{19}
\indexentry {AssociatorSubloop@`AssociatorSubloop'}{20}
\indexentry {Normal subloops@Normal subloops|indexit}{20}
\indexentry {normal subloop}{20}
\indexentry {IsNormal@`IsNormal'}{20}
\indexentry {normal closure}{20}
\indexentry {NormalClosure@`NormalClosure'}{20}
\indexentry {simple loop}{20}
\indexentry {IsSimple@`IsSimple'}{20}
\indexentry {Factor loops@Factor loops|indexit}{20}
\indexentry {FactorLoop@`FactorLoop'}{20}
\indexentry {NaturalHomomorphismByNormalSubloop@`NaturalHomomorphismByNormalSubloop'}{20}
\indexentry {Nilpotency and central series@Nilpotency and central series|indexit}{20}
\indexentry {NilpotencyClassOfLoop@`NilpotencyClassOfLoop'}{20}
\indexentry {IsNilpotent@`IsNilpotent'}{20}
\indexentry {strongly nilpotent loop}{20}
\indexentry {IsStronglyNilpotent@`IsStronglyNilpotent'}{20}
\indexentry {iterated centers}{20}
\indexentry {upper central series}{20}
\indexentry {UpperCentralSeries@`UpperCentralSeries'}{20}
\indexentry {lower central series}{20}
\indexentry {LowerCentralSeries@`LowerCentralSeries'}{20}
\indexentry {Solvability@Solvability|indexit}{21}
\indexentry {IsSolvable@`IsSolvable'}{21}
\indexentry {DerivedSubloop@`DerivedSubloop'}{21}
\indexentry {DerivedLength@`DerivedLength'}{21}
\indexentry {FrattiniSubloop@`FrattiniSubloop'}{21}
\indexentry {FrattinifactorSize@`FrattinifactorSize'}{21}
\indexentry {Isomorphisms and automorphisms@Isomorphisms and automorphisms|indexit}{21}
\indexentry {IsomorphismLoops@`IsomorphismLoops'}{21}
\indexentry {AutomorphismGroup@`AutomorphismGroup'}{21}
\indexentry {How are isomorphisms computed@How are isomorphisms computed|indexit}{21}
\indexentry {Discriminator@`Discriminator'}{21}
\indexentry {AreEqualDiscriminators@`AreEqualDiscriminators'}{21}
\indexentry {Associativity, commutativity and generalizations@Associativity, commutativity and generalizations|indexit}{22}
\indexentry {IsAssociative@`IsAssociative'}{22}
\indexentry {IsCommutative@`IsCommutative'}{22}
\indexentry {power-associative loop}{22}
\indexentry {diassociative loop}{22}
\indexentry {IsPowerAssociative@`IsPowerAssociative'}{22}
\indexentry {IsDiassociative@`IsDiassociative'}{22}
\indexentry {Inverse properties@Inverse properties|indexit}{22}
\indexentry {left inverse property}{22}
\indexentry {right inverse property}{22}
\indexentry {inverse property}{22}
\indexentry {two-sided inverses}{22}
\indexentry {HasLeftInverseProperty@`HasLeftInverseProperty'}{22}
\indexentry {HasRightInverseProperty@`HasRightInverseProperty'}{22}
\indexentry {HasInverseProperty@`HasInverseProperty'}{22}
\indexentry {HasTwosidedInverses@`HasTwosidedInverses'}{22}
\indexentry {weak inverse property}{22}
\indexentry {HasWeakInverseProperty@`HasWeakInverseProperty'}{22}
\indexentry {automorphic inverse property}{22}
\indexentry {antiautomorphic inverse property}{22}
\indexentry {HasAutomorphicInverseProperty@`HasAutomorphicInverseProperty'}{22}
\indexentry {HasAntiautomorphicInverseProperty@`HasAntiautomorphicInverseProperty'}{22}
\indexentry {Some properties of quasigroups@Some properties of quasigroups|indexit}{22}
\indexentry {semisymmetric quasigroup}{22}
\indexentry {totally symmetric quasigroup}{22}
\indexentry {IsSemisymmetric@`IsSemisymmetric'}{23}
\indexentry {IsTotallySymmetric@`IsTotallySymmetric'}{23}
\indexentry {idempotent quasigroup}{23}
\indexentry {Steiner quasigroup}{23}
\indexentry {unipotent quasigroup}{23}
\indexentry {IsIdempotent@`IsIdempotent'}{23}
\indexentry {IsSteinerQuasigroup@`IsSteinerQuasigroup'}{23}
\indexentry {IsUnipotent@`IsUnipotent'}{23}
\indexentry {left distributive quasigroup}{23}
\indexentry {right distributive quasigroup}{23}
\indexentry {distributive quasigroup}{23}
\indexentry {entropic quasigroup}{23}
\indexentry {medial quasigroup}{23}
\indexentry {IsLeftDistributive@`IsLeftDistributive'}{23}
\indexentry {IsRightDistributive@`IsRightDistributive'}{23}
\indexentry {IsDistributive@`IsDistributive'}{23}
\indexentry {IsEntropic@`IsEntropic'}{23}
\indexentry {IsMedial@`IsMedial'}{23}
\indexentry {IsLDistributive@`IsLDistributive'}{23}
\indexentry {IsRDistributive@`IsRDistributive'}{23}
\indexentry {Loops of Bol-Moufang type@Loops of Bol-Moufang type|indexit}{23}
\indexentry {loops of Bol-Moufang type}{23}
\indexentry {identity of Bol-Moufang type}{23}
\indexentry {left alternative loops}{23}
\indexentry {right alternative loops}{23}
\indexentry {left nuclear square loops}{23}
\indexentry {middle nuclear square loops}{23}
\indexentry {right nuclear square loops}{23}
\indexentry {flexible loops}{23}
\indexentry {left Bol loops}{23}
\indexentry {right Bol loops}{23}
\indexentry {LC-loops}{23}
\indexentry {RC-loops}{23}
\indexentry {Moufang loops}{23}
\indexentry {C-loops}{23}
\indexentry {extra loops}{23}
\indexentry {alternative loop}{23}
\indexentry {nuclear square loop}{23}
\indexentry {IsExtraLoop@`IsExtraLoop'}{24}
\indexentry {IsMoufangLoop@`IsMoufangLoop'}{24}
\indexentry {IsCLoop@`IsCLoop'}{24}
\indexentry {IsLeftBolLoop@`IsLeftBolLoop'}{24}
\indexentry {IsRightBolLoop@`IsRightBolLoop'}{24}
\indexentry {IsLCLoop@`IsLCLoop'}{24}
\indexentry {IsRCLoop@`IsRCLoop'}{24}
\indexentry {IsLeftNuclearSquareLoop@`IsLeftNuclearSquareLoop'}{24}
\indexentry {IsMiddleNuclearSquareLoop@`IsMiddleNuclearSquareLoop'}{24}
\indexentry {IsRightNuclearSquareLoop@`IsRightNuclearSquareLoop'}{24}
\indexentry {IsNuclearSquareLoop@`IsNuclearSquareLoop'}{24}
\indexentry {IsFlexible@`IsFlexible'}{24}
\indexentry {IsLeftAlternative@`IsLeftAlternative'}{24}
\indexentry {IsRightAlternative@`IsRightAlternative'}{24}
\indexentry {IsAlternative@`IsAlternative'}{24}
\indexentry {Power alternative loops@Power alternative loops|indexit}{24}
\indexentry {left power alternative loop}{24}
\indexentry {right power alternative loop}{24}
\indexentry {power alternative loop}{24}
\indexentry {IsLeftPowerAlternative@`IsLeftPowerAlternative'}{24}
\indexentry {IsRightPowerAlternative@`IsRightPowerAlternative'}{24}
\indexentry {IsPowerAlternative@`IsPowerAlternative'}{24}
\indexentry {Conjugacy closed loops and related properties@Conjugacy closed loops and related properties|indexit}{24}
\indexentry {left conjugacy closed loop}{24}
\indexentry {right conjugacy closed loop}{24}
\indexentry {conjugacy closed loop}{24}
\indexentry {IsLCCLoop@`IsLCCLoop'}{24}
\indexentry {IsRCCLoop@`IsRCCLoop'}{24}
\indexentry {IsCCLoop@`IsCCLoop'}{24}
\indexentry {Osborn loop}{25}
\indexentry {IsOsbornLoop@`IsOsbornLoop'}{25}
\indexentry {Additional varieties of loops@Additional varieties of loops|indexit}{25}
\indexentry {left Bruck loop}{25}
\indexentry {right Bruck loop}{25}
\indexentry {K-loop}{25}
\indexentry {IsLeftBruckLoop@`IsLeftBruckLoop'}{25}
\indexentry {IsLeftKLoop@`IsLeftKLoop'}{25}
\indexentry {IsRightBruckLoop@`IsRightBruckLoop'}{25}
\indexentry {IsRightKLoop@`IsRightKLoop'}{25}
\indexentry {Steiner loop}{25}
\indexentry {IsSteinerLoop@`IsSteinerLoop'}{25}
\indexentry {Moufang modifications@Moufang modifications|indexit}{26}
\indexentry {Moufang modifications}{26}
\indexentry {cyclic modification}{26}
\indexentry {LoopByCyclicModification@`LoopByCyclicModification'}{26}
\indexentry {dihedral modification}{26}
\indexentry {LoopByDihedralModification@`LoopByDihedralModification'}{26}
\indexentry {LoopMG2@`LoopMG2'}{26}
\indexentry {Triality for Moufang loops@Triality for Moufang loops|indexit}{26}
\indexentry {group with triality}{26}
\indexentry {TrialityPermGroup@`TrialityPermGroup'}{26}
\indexentry {TrialityPcGroup@`TrialityPcGroup'}{27}
\indexentry {A typical library@A typical library|indexit}{28}
\indexentry {MyLibraryLoop@`MyLibraryLoop'}{28}
\indexentry {LibraryLoop@`LibraryLoop'}{28}
\indexentry {DisplayLibraryInfo@`DisplayLibraryInfo'}{28}
\indexentry {Left Bol loops@Left Bol loops|indexit}{28}
\indexentry {LeftBolLoop@`LeftBolLoop'}{28}
\indexentry {Small Moufang loops@Small Moufang loops|indexit}{28}
\indexentry {MoufangLoop@`MoufangLoop'}{28}
\indexentry {octonion loop}{29}
\indexentry {octonions}{29}
\indexentry {IsomorphismTypeOfMoufangLoop@`IsomorphismTypeOfMoufangLoop'}{29}
\indexentry {Steiner loops@Steiner loops|indexit}{29}
\indexentry {SteinerLoop@`SteinerLoop'}{29}
\indexentry {CC-loops@CC-loops|indexit}{29}
\indexentry {conjugacy closed loop}{29}
\indexentry {CCLoop@`CCLoop'}{30}
\indexentry {Paige loops@Paige loops|indexit}{30}
\indexentry {Paige loop}{30}
\indexentry {PaigeLoop@`PaigeLoop'}{30}
\indexentry {Interesting loops@Interesting loops|indexit}{30}
\indexentry {sedenions}{30}
\indexentry {InterestingLoop@`InterestingLoop'}{30}
\indexentry {list of files}{31}
