\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 {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}{16}
\indexentry {Parent@`Parent'}{16}
\indexentry {Position@`Position'}{16}
\indexentry {PosInParent@`PosInParent'}{16}
\indexentry {Comparing quasigroups with common parent@Comparing quasigroups with common parent|indexit}{16}
\indexentry {Subquasigroups and subloops@Subquasigroups and subloops|indexit}{16}
\indexentry {Subquasigroup@`Subquasigroup'}{16}
\indexentry {Subloop@`Subloop'}{16}
\indexentry {IsSubquasigroup@`IsSubquasigroup'}{16}
\indexentry {IsSubloop@`IsSubloop'}{16}
\indexentry {Translations and sections@Translations and sections|indexit}{17}
\indexentry {LeftTranslation@`LeftTranslation'}{17}
\indexentry {RightTranslation@`RightTranslation'}{17}
\indexentry {LeftSection@`LeftSection'}{17}
\indexentry {RightSection@`RightSection'}{17}
\indexentry {Multiplication groups@Multiplication groups|indexit}{17}
\indexentry {LeftMultiplicationGroup@`LeftMultiplicationGroup'}{17}
\indexentry {RightMultiplicationGroup@`RightMultiplicationGroup'}{17}
\indexentry {MultiplicationGroup@`MultiplicationGroup'}{17}
\indexentry {relative left multiplication group}{17}
\indexentry {relative right multiplication group}{17}
\indexentry {relative multiplication group}{17}
\indexentry {RelativeLeftMultiplicationGroup@`RelativeLeftMultiplicationGroup'}{18}
\indexentry {RelativeRightMultiplicationGroup@`RelativeRightMultiplicationGroup'}{18}
\indexentry {RelativeMultiplicationGroup@`RelativeMultiplicationGroup'}{18}
\indexentry {Inner mapping groups@Inner mapping groups|indexit}{18}
\indexentry {inner mapping group}{18}
\indexentry {left inner mapping group}{18}
\indexentry {right inner mapping group}{18}
\indexentry {InnerMappingGroup@`InnerMappingGroup'}{18}
\indexentry {LeftInnerMappingGroup@`LeftInnerMappingGroup'}{18}
\indexentry {RightInnerMappingGroup@`RightInnerMappingGroup'}{18}
\indexentry {Nuclei, commutant, center, and associator subloop@Nuclei, commutant, center, and associator subloop|indexit}{18}
\indexentry {left nucleus}{18}
\indexentry {middle nucleus}{18}
\indexentry {right nucleus}{18}
\indexentry {nucleus}{18}
\indexentry {LeftNucleus@`LeftNucleus'}{18}
\indexentry {MiddleNucleus@`MiddleNucleus'}{18}
\indexentry {RightNucleus@`RightNucleus'}{18}
\indexentry {Nuc@`Nuc'}{18}
\indexentry {NucleusOfLoop@`NucleusOfLoop'}{18}
\indexentry {NucleusOfQuasigroup@`NucleusOfQuasigroup'}{18}
\indexentry {commutant}{18}
\indexentry {Moufang center}{18}
\indexentry {Commutant@`Commutant'}{18}
\indexentry {Center@`Center'}{18}
\indexentry {associator subloop}{18}
\indexentry {AssociatorSubloop@`AssociatorSubloop'}{19}
\indexentry {Normal subloops@Normal subloops|indexit}{19}
\indexentry {normal subloop}{19}
\indexentry {IsNormal@`IsNormal'}{19}
\indexentry {normal closure}{19}
\indexentry {NormalClosure@`NormalClosure'}{19}
\indexentry {simple loop}{19}
\indexentry {IsSimple@`IsSimple'}{19}
\indexentry {Factor loops@Factor loops|indexit}{19}
\indexentry {FactorLoop@`FactorLoop'}{19}
\indexentry {NaturalHomomorphismByNormalSubloop@`NaturalHomomorphismByNormalSubloop'}{19}
\indexentry {Nilpotency and central series@Nilpotency and central series|indexit}{19}
\indexentry {NilpotencyClassOfLoop@`NilpotencyClassOfLoop'}{19}
\indexentry {IsNilpotent@`IsNilpotent'}{19}
\indexentry {strongly nilpotent loop}{19}
\indexentry {IsStronglyNilpotent@`IsStronglyNilpotent'}{19}
\indexentry {iterated centers}{19}
\indexentry {upper central series}{19}
\indexentry {UpperCentralSeries@`UpperCentralSeries'}{19}
\indexentry {lower central series}{19}
\indexentry {LowerCentralSeries@`LowerCentralSeries'}{19}
\indexentry {Solvability@Solvability|indexit}{19}
\indexentry {IsSolvable@`IsSolvable'}{20}
\indexentry {DerivedSubloop@`DerivedSubloop'}{20}
\indexentry {DerivedLength@`DerivedLength'}{20}
\indexentry {FrattiniSubloop@`FrattiniSubloop'}{20}
\indexentry {FrattinifactorSize@`FrattinifactorSize'}{20}
\indexentry {Isomorphisms and automorphisms@Isomorphisms and automorphisms|indexit}{20}
\indexentry {IsomorphismLoops@`IsomorphismLoops'}{20}
\indexentry {AutomorphismGroup@`AutomorphismGroup'}{20}
\indexentry {How are isomorphisms computed@How are isomorphisms computed|indexit}{20}
\indexentry {Discriminator@`Discriminator'}{20}
\indexentry {AreEqualDiscriminators@`AreEqualDiscriminators'}{20}
\indexentry {Associativity, commutativity and generalizations@Associativity, commutativity and generalizations|indexit}{21}
\indexentry {IsAssociative@`IsAssociative'}{21}
\indexentry {IsCommutative@`IsCommutative'}{21}
\indexentry {power-associative loop}{21}
\indexentry {diassociative loop}{21}
\indexentry {IsPowerAssociative@`IsPowerAssociative'}{21}
\indexentry {IsDiassociative@`IsDiassociative'}{21}
\indexentry {Inverse properties@Inverse properties|indexit}{21}
\indexentry {left inverse property}{21}
\indexentry {right inverse property}{21}
\indexentry {inverse property}{21}
\indexentry {two-sided inverses}{21}
\indexentry {HasLeftInverseProperty@`HasLeftInverseProperty'}{21}
\indexentry {HasRightInverseProperty@`HasRightInverseProperty'}{21}
\indexentry {HasInverseProperty@`HasInverseProperty'}{21}
\indexentry {HasTwosidedInverses@`HasTwosidedInverses'}{21}
\indexentry {weak inverse property}{21}
\indexentry {HasWeakInverseProperty@`HasWeakInverseProperty'}{21}
\indexentry {automorphic inverse property}{21}
\indexentry {antiautomorphic inverse property}{21}
\indexentry {HasAutomorphicInverseProperty@`HasAutomorphicInverseProperty'}{21}
\indexentry {HasAntiautomorphicInverseProperty@`HasAntiautomorphicInverseProperty'}{21}
\indexentry {Some properties of quasigroups@Some properties of quasigroups|indexit}{21}
\indexentry {semisymmetric quasigroup}{21}
\indexentry {totally symmetric quasigroup}{21}
\indexentry {IsSemisymmetric@`IsSemisymmetric'}{22}
\indexentry {IsTotallySymmetric@`IsTotallySymmetric'}{22}
\indexentry {idempotent quasigroup}{22}
\indexentry {Steiner quasigroup}{22}
\indexentry {unipotent quasigroup}{22}
\indexentry {IsIdempotent@`IsIdempotent'}{22}
\indexentry {IsSteinerQuasigroup@`IsSteinerQuasigroup'}{22}
\indexentry {IsUnipotent@`IsUnipotent'}{22}
\indexentry {left distributive quasigroup}{22}
\indexentry {right distributive quasigroup}{22}
\indexentry {distributive quasigroup}{22}
\indexentry {entropic quasigroup}{22}
\indexentry {medial quasigroup}{22}
\indexentry {IsLeftDistributive@`IsLeftDistributive'}{22}
\indexentry {IsRightDistributive@`IsRightDistributive'}{22}
\indexentry {IsDistributive@`IsDistributive'}{22}
\indexentry {IsEntropic@`IsEntropic'}{22}
\indexentry {IsMedial@`IsMedial'}{22}
\indexentry {IsLDistributive@`IsLDistributive'}{22}
\indexentry {IsRDistributive@`IsRDistributive'}{22}
\indexentry {Loops of Bol-Moufang type and related properties@Loops of Bol-Moufang type and related properties|indexit}{22}
\indexentry {loops of Bol-Moufang type}{22}
\indexentry {identity of Bol-Moufang type}{22}
\indexentry {left alternative loops}{22}
\indexentry {right alternative loops}{22}
\indexentry {left nuclear square loops}{22}
\indexentry {middle nuclear square loops}{22}
\indexentry {right nuclear square loops}{22}
\indexentry {flexible loops}{22}
\indexentry {left Bol loops}{22}
\indexentry {right Bol loops}{22}
\indexentry {LC-loops}{22}
\indexentry {RC-loops}{22}
\indexentry {Moufang loops}{22}
\indexentry {C-loops}{22}
\indexentry {extra loops}{22}
\indexentry {alternative loop}{22}
\indexentry {nuclear square loop}{22}
\indexentry {IsExtraLoop@`IsExtraLoop'}{23}
\indexentry {IsMoufangLoop@`IsMoufangLoop'}{23}
\indexentry {IsCLoop@`IsCLoop'}{23}
\indexentry {IsLeftBolLoop@`IsLeftBolLoop'}{23}
\indexentry {IsRightBolLoop@`IsRightBolLoop'}{23}
\indexentry {IsLCLoop@`IsLCLoop'}{23}
\indexentry {IsRCLoop@`IsRCLoop'}{23}
\indexentry {IsLeftNuclearSquareLoop@`IsLeftNuclearSquareLoop'}{23}
\indexentry {IsMiddleNuclearSquareLoop@`IsMiddleNuclearSquareLoop'}{23}
\indexentry {IsRightNuclearSquareLoop@`IsRightNuclearSquareLoop'}{23}
\indexentry {IsNuclearSquareLoop@`IsNuclearSquareLoop'}{23}
\indexentry {IsFlexible@`IsFlexible'}{23}
\indexentry {IsLeftAlternative@`IsLeftAlternative'}{23}
\indexentry {IsRightAlternative@`IsRightAlternative'}{23}
\indexentry {IsAlternative@`IsAlternative'}{23}
\indexentry {Conjugacy closed loops and related properties@Conjugacy closed loops and related properties|indexit}{23}
\indexentry {left conjugacy closed loop}{23}
\indexentry {right conjugacy closed loop}{23}
\indexentry {conjugacy closed loop}{23}
\indexentry {IsLCCLoop@`IsLCCLoop'}{23}
\indexentry {IsRCCLoop@`IsRCCLoop'}{23}
\indexentry {IsCCLoop@`IsCCLoop'}{23}
\indexentry {Osborn loop}{23}
\indexentry {IsOsbornLoop@`IsOsbornLoop'}{23}
\indexentry {Additional varieties of loops@Additional varieties of loops|indexit}{23}
\indexentry {left Bruck loop}{23}
\indexentry {right Bruck loop}{23}
\indexentry {K-loop}{23}
\indexentry {IsLeftBruckLoop@`IsLeftBruckLoop'}{24}
\indexentry {IsLeftKLoop@`IsLeftKLoop'}{24}
\indexentry {IsRightBruckLoop@`IsRightBruckLoop'}{24}
\indexentry {IsRightKLoop@`IsRightKLoop'}{24}
\indexentry {Steiner loop}{24}
\indexentry {IsSteinerLoop@`IsSteinerLoop'}{24}
\indexentry {Moufang modifications@Moufang modifications|indexit}{25}
\indexentry {Moufang modifications}{25}
\indexentry {cyclic modification}{25}
\indexentry {LoopByCyclicModification@`LoopByCyclicModification'}{25}
\indexentry {dihedral modification}{25}
\indexentry {LoopByDihedralModification@`LoopByDihedralModification'}{25}
\indexentry {LoopMG2@`LoopMG2'}{25}
\indexentry {Triality for Moufang loops@Triality for Moufang loops|indexit}{25}
\indexentry {group with triality}{25}
\indexentry {TrialityPermGroup@`TrialityPermGroup'}{25}
\indexentry {TrialityPcGroup@`TrialityPcGroup'}{26}
\indexentry {A typical library@A typical library|indexit}{27}
\indexentry {MyLibraryLoop@`MyLibraryLoop'}{27}
\indexentry {LibraryLoop@`LibraryLoop'}{27}
\indexentry {DisplayLibraryInfo@`DisplayLibraryInfo'}{27}
\indexentry {Left Bol loops@Left Bol loops|indexit}{27}
\indexentry {LeftBolLoop@`LeftBolLoop'}{27}
\indexentry {Small Moufang loops@Small Moufang loops|indexit}{27}
\indexentry {MoufangLoop@`MoufangLoop'}{27}
\indexentry {octonion loop}{28}
\indexentry {octonions}{28}
\indexentry {IsomorphismTypeOfMoufangLoop@`IsomorphismTypeOfMoufangLoop'}{28}
\indexentry {Steiner loops@Steiner loops|indexit}{28}
\indexentry {SteinerLoop@`SteinerLoop'}{28}
\indexentry {CC-loops@CC-loops|indexit}{28}
\indexentry {conjugacy closed loop}{28}
\indexentry {CCLoop@`CCLoop'}{29}
\indexentry {Paige loops@Paige loops|indexit}{29}
\indexentry {Paige loop}{29}
\indexentry {PaigeLoop@`PaigeLoop'}{29}
\indexentry {Interesting loops@Interesting loops|indexit}{29}
\indexentry {sedenions}{29}
\indexentry {InterestingLoop@`InterestingLoop'}{29}
\indexentry {list of files}{30}
