- alternative loop, 2.10
- antiautomorphic inverse property,
2.10
- AreEqualDiscriminators, 3.1
- AsGroup, 2.2
- AsLoop, 1.5, 2.2
- AsQuasigroup, 1.5,
2.2
- Associator, 2.5
- associator, 2.5
- associator subloop, 2.9
- AssociatorSubloop, 2.9
- AutomorphismGroup, 3.1
- Cayley table, 2.2
- CayleyTable, 2.4
- Center, 2.9
- Commutant, 2.9
- commutant, 2.9
- Commutator, 2.5
- commutator, 2.5
- conjugacy closed loop, 2.10
- cyclic modification, 3.2
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- DerivedLength, 2.14
- DerivedSubloop, 2.14
- diassoicativy, 2.10
- dihedral modification, 3.2
- DirectProduct, 2.2
- Discriminator, 3.1
- DisplayLibraryInfo, 4.1
- distributive quasigroup,
2.10
- EfficientGenerators, 3.1
- Elements, 2.4
- entropic quasigroup, 2.10
- Exponent, 2.4
- exponent, 2.4
- FactorLoop, 2.12
- FrattinifactorSize, 2.14
- FrattiniSubloop, 2.14
- GeneratorsOfLoop, 2.6
- GeneratorsOfQuasigroup, 2.6
- group, 1.4
- groupoid, 1.4
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- HasAntiautomorphicInverseProperty,
2.10
- HasAutomorphicInverseProperty,
2.10
- HasInverseProperty, 2.10
- HasLeftInverseProperty, 2.10
- HasRightInverseProperty,
2.10
- HasTwosidedInverses, 2.10
- homomorphism, 1.4
- homotopism, 1.4
- idempotent, 2.10
- identity element, 1.4
- inner mapping group, 2.7
- InnerMappingGroup, 2.7
- InterestingLoop, 4.6
- Inverse, 2.5
- inverse, 2.5
- inverse property, 2.10
- IsAlternative, 2.10
- IsAssociative, 2.10
- IsCCLoop, 2.10
- IsCLoop, 2.10
- IsCommutative, 2.10
- IsDiassociative, 2.10
- IsDistributive, 2.10
- IsEntropic, 2.10
- IsExtraLoop, 2.10
- IsFlexible, 2.10
- IsIdempotent, 2.10
- IsLCCLoop, 2.10
- IsLCLoop, 2.10
- IsLDistributive, 2.10
- IsLeftAlternative, 2.10
- IsLeftBolLoop, 2.10
- IsLeftBruckLoop, 2.10
- IsLeftDistributive, 2.10
- IsLeftKLoop, 2.10
- IsLeftNuclearSquareLoop,
2.10
- IsLoop, 2.3
- IsLoopCayleyTable, 2.2
- IsLoopElement, 2.3
- IsLoopTable, 2.2
- IsMedial, 2.10
- IsMiddleNuclearSquareLoop,
2.10
- IsMoufangLoop, 2.10
- IsNilpotent, 2.13
- IsNormal, 2.11
- IsNuclearSquareLoop, 2.10
- isomorphism, 1.4
- IsomorphismLoops, 3.1
- IsomorphismTypeOfMoufangLoop,
4.3
- isotopism, 1.4
- IsPowerAssociative, 2.10
- IsQuasigroup, 2.3
- IsQuasigroupCayleyTable, 2.2
- IsQuasigroupElement, 2.3
- IsQuasigroupTable, 2.2
- IsRCCLoop, 2.10
- IsRCLoop, 2.10
- IsRDistributive, 2.10
- IsRightAlternative, 2.10
- IsRightBolLoop, 2.10
- IsRightBruckLoop, 2.10
- IsRightDistributive, 2.10
- IsRightKLoop, 2.10
- IsRightNuclearSquareLoop,
2.10
- IsSemisymmetric, 2.10
- IsSimple, 2.11
- IsSolvable, 2.14
- IsSteinerLoop, 2.10
- IsSteinerQuasigroup, 2.10
- IsStronglyNilpotent, 2.13
- IsSubloop, 2.8
- IsSubquasigroup, 2.8
- IsTotallySymmetric, 2.10
- IsUnipotent, 2.10
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- K-loop, 2.10
- Latin square, 1.4
- left Bruck loop, 2.10
- left conjugacy closed loop,
2.10
- left division, 2.5
- left inverse, 2.5
- left inverse property, 2.10
- left nucleus, 2.9
- left section, 1.4
- left translation, 1.4
- LeftBolLoop, 4.1,
4.2
- LeftDivision, 2.5
- LeftInverse, 2.5
- LeftMultiplicationGroup, 2.7
- LeftNucleus, 2.9
- LeftSection, 2.7
- LeftTranslation, 2.7
- LibraryLoop, 4.1
- list of files, 1.1
- loop, 1.4
- LoopByCayleyTable, 2.2
- LoopByCyclicModification,
3.2
- LoopByDihedralModification,
3.2
- LoopFromFile, 2.2
- LoopMG2, 3.2
- loops of Bol-Moufang type,
2.10
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- magma, 1.4
- middle nucleus, 2.9
- MiddleNucleus, 2.9
- monoassociative, 2.5
- monoid, 1.4
- Moufang center, 2.9
- Moufang modifications, 3.2
- MoufangLoop, 4.3
- multiplication group, 1.4
- MultiplicationGroup, 2.7
- MultiplicativeNeutralElement,
2.4
- MyLibraryLoop, 4.1
- NaturalHomomorphismByNormalSubloop,
2.12
- neutral element, 1.4
- NilpotencyClassOfLoop, 2.13
- normal closure, 2.11
- normal subloop, 2.11
- NormalClosure, 2.11
- normalized Latin square, 2.2
- NormalizedQuasigroupTable,
2.2
- Nuc, 2.9
- nuclear square loop, 2.10
- nucleus, 2.9
- NucleusOfLoop, 2.9
- NucleusOfQuasigroup, 2.9
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- octonions, 4.3
- One, 2.4
- Opposite, 2.2
- opposite quasigroup, 2.2
- Paige loop, 4.5
- PaigeLoop, 4.5
- Parent, 2.8
- PosInParent, 2.8
- power associative, 2.5
- power associativity, 2.10
- principal loop isotope, 1.4
- PrincipalLoopIsotope, 2.2
- quasigroup, 1.4
- QuasigroupByCayleyTable, 2.2
- QuasigroupFromFile, 2.2
- RelativeLeftMultiplicationGroup,
2.7
- RelativeMultiplicationGroup,
2.7
- RelativeRightMultiplicationGroup,
2.7
- right Bruck loop, 2.10
- right conjugacy closed loop,
2.10
- right distributive quasigroup,
2.10
- right division, 2.5
- right inverse, 2.5
- right inverse property, 2.10
- right multiplication group,
1.4
- right nucleus, 2.9
- right section, 1.4
- right translation, 1.4
- RightDivision, 2.5
- RightInverse, 2.5
- RightMultiplicationGroup,
2.7
- RightNucleus, 2.9
- RightSection, 2.7
- RightTranslation, 2.7
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- sedenions, 4.6
- semigroup, 1.4
- SetLoopElmName, 2.1
- SetQuasigroupElmName, 2.1
- simple loop, 2.11
- Size, 2.4
- SmallGeneratingSet, 2.6
- Steiner loop, 2.10
- Steiner quasigroup, 2.10
- SteinerLoop, 4.4
- Subloop, 2.8
- Subquasigroup, 2.8
- TrialityPcGroup, 3.3
- TrialityPermGroup, 3.3
- two-sided inverse, 1.4
- two-sided inverses, 2.10
- unipotent quasigroup, 2.10
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