GAP (Loops) - Index

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### Index

`AllLoopsWithMltGroup` 8.4-5
`AllLoopTablesInGroup` 8.4-1
`AllProperLoopTablesInGroup` 8.4-2
`AllSubloops` 6.2-5
`AllSubquasigroups` 6.2-4
alternative loop 7.4
left 7.4
right 7.4
antiautomorphic inverse property 7.2-5
`AreEqualDiscriminators` 6.11-11
`AssociatedLeftBruckLoop` 8.1-1
`AssociatedRightBruckLoop` 8.1-1
associator 2.5
`Associator` 5.4-1
associator subloop 2.5
`AssociatorSubloop` 6.6-5
automorphic inverse property 7.2-4
automorphic loop 7.7
left 7.7
middle 7.7
right 7.7
`AutomorphicLoop` 9.11-1
`AutomorphismGroup` 6.11-5
Bol loop, left 3.3 7.4 8.1-1
right 7.4
Bruck loop, associated left 8.1-1
left 7.8-3
right 7.8-4
C loop 7.4
`CanonicalCayleyTable` 4.3-1
`CanonicalCopy` 4.3-2
Cayley table 4.1
canonical 4.3-1
`CayleyTable` 5.1-2
`CayleyTableByPerms` 4.6-1
`CCLoop` 9.7-3
center 2.3
`Center` 6.6-4
central series, lower 6.9-5
upper 2.4
Chein loop 8.2-3
cocycle 4.8
code loop 7.8-1
`CodeLoop` 9.5-1
commutant 2.3
`Commutant` 6.6-3
commutator 2.5
`Commutator` 5.4-2
conjugacy closed loop 7.6
left 7.6
right 7.6
`ConjugacyClosedLoop` 9.7-3
conjugation 6.5
coset 6.2-6
derived series 2.4
derived subloop 2.4
`DerivedLength` 6.10-3
`DerivedSubloop` 6.10-2
diassociative quasigroup 7.1-4
`DirectProduct` 4.11-1
`Discriminator` 6.11-10
`DisplayLibraryInfo` 9.1-3
distributive quasigroup 7.3-6
left 7.3-6
right 7.3-6
division, left 2.2
right 2.2
`Elements` 5.1-1
entropic quasigroup 7.3-7
exact group factorization 8.1-2
exponent 5.1-5
`Exponent` 5.1-5
extension 4.8
nuclear 4.8
extra loop 7.4
`FactorLoop` 6.8-1
flexible loop 7.4
folder, quasigroup 4.7
Frattini subloop 6.10-4
`FrattinifactorSize` 6.10-5
`FrattiniSubloop` 6.10-4
`GeneratorsOfLoop` 5.5-1
`GeneratorsOfQuasigroup` 5.5-1
`GeneratorsSmallest` 5.5-2
group 2.1
group with triality 8.3
groupoid 2.1
`HasAntiautomorphicInverseProperty` 7.2-5
`HasAutomorphicInverseProperty` 7.2-4
`HasInverseProperty` 7.2-1
`HasLeftInverseProperty` 7.2-1
`HasRightInverseProperty` 7.2-1
`HasTwosidedInverses` 7.2-2
`HasWeakInverseProperty` 7.2-3
homomorphism 2.6
homotopism 2.6
idempotent quasigroup 7.3-3
identity, element 2.1
of Bol-Moufang type 7.4
inner mapping, left 6.5
middle 6.5
right 6.5
inner mapping group 2.2
left 2.2
middle 6.5
right 2.2
`InnerMappingGroup` 6.5-3
`InterestingLoop` 9.12-1
`IntoGroup` 4.10-4
`IntoLoop` 4.10-3
`IntoQuasigroup` 4.10-1
inverse 5.3
`Inverse` 5.3-1
inverse, left 5.3 7.2
right 5.3 7.2
two-sided 2.1 7.2-2
inverse property 7.2-1
antiautomorphic 7.2-5
automorphic 7.2-4
left 7.2-1
right 7.2-1
weak 7.2-3
`IsALoop` 7.7-4
`IsAlternative` 7.4-15
`IsAssociative` 7.1-1
`IsAutomorphicLoop` 7.7-4
`IsCCLoop` 7.6-3
`IsCLoop` 7.4-3
`IsCodeLoop` 7.8-1
`IsCommutative` 7.1-2
`IsConjugacyClosedLoop` 7.6-3
`IsDiassociative` 7.1-4
`IsDistributive` 7.3-6
`IsEntropic` 7.3-7
`IsExactGroupFactorization` 8.1-2
`IsExtraLoop` 7.4-1
`IsFlexible` 7.4-12
`IsIdempotent` 7.3-3
`IsLCCLoop` 7.6-1
`IsLCLoop` 7.4-6
`IsLeftALoop` 7.7-1
`IsLeftAlternative` 7.4-13
`IsLeftAutomorphicLoop` 7.7-1
`IsLeftBolLoop` 7.4-4
`IsLeftBruckLoop` 7.8-3
`IsLeftConjugacyClosedLoop` 7.6-1
`IsLeftDistributive` 7.3-6
`IsLeftKLoop` 7.8-3
`IsLeftNuclearSquareLoop` 7.4-8
`IsLeftPowerAlternative` 7.5-1
IsLoop 3.1
`IsLoopCayleyTable` 4.2-2
IsLoopElement 3.1
`IsLoopTable` 4.2-2
`IsMedial` 7.3-7
`IsMiddleALoop` 7.7-2
`IsMiddleAutomorphicLoop` 7.7-2
`IsMiddleNuclearSquareLoop` 7.4-9
`IsMoufangLoop` 7.4-2
`IsNilpotent` 6.9-1
`IsNormal` 6.7-1
`IsNuclearSquareLoop` 7.4-11
`IsomorphicCopyByNormalSubloop` 6.11-9
`IsomorphicCopyByPerm` 6.11-8
isomorphism 2.6
`IsomorphismLoops` 6.11-2
`IsomorphismQuasigroups` 6.11-1
`IsOsbornLoop` 7.6-4
isotopism 2.6
principal 2.6
`IsotopismLoops` 6.12-1
`IsPowerAlternative` 7.5-1
`IsPowerAssociative` 7.1-3
IsQuasigroup 3.1
`IsQuasigroupCayleyTable` 4.2-1
IsQuasigroupElement 3.1
`IsQuasigroupTable` 4.2-1
`IsRCCLoop` 7.6-2
`IsRCLoop` 7.4-7
`IsRightALoop` 7.7-3
`IsRightAlternative` 7.4-14
`IsRightAutomorphicLoop` 7.7-3
`IsRightBolLoop` 7.4-5
`IsRightBruckLoop` 7.8-4
`IsRightConjugacyClosedLoop` 7.6-2
`IsRightDistributive` 7.3-6
`IsRightKLoop` 7.8-4
`IsRightNuclearSquareLoop` 7.4-10
`IsRightPowerAlternative` 7.5-1
`IsSemisymmetric` 7.3-1
`IsSimple` 6.7-3
`IsSolvable` 6.10-1
`IsSteinerLoop` 7.8-2
`IsSteinerQuasigroup` 7.3-4
`IsStronglyNilpotent` 6.9-3
`IsSubloop` 6.2-3
`IsSubquasigroup` 6.2-3
`IsTotallySymmetric` 7.3-2
`IsUnipotent` 7.3-5
`ItpSmallLoop` 9.13-1
K loop, left 7.8-3
right 7.8-4
latin square 2.1 4.1
random 4.9
LC loop 7.4
`LCCLoop` 9.7-2
`LeftBolLoop` 9.2-1
`LeftBruckLoop` 9.3-1
`LeftConjugacyClosedLoop` 9.7-2
`LeftDivision` 5.2-1 5.2-1 5.2-1
`LeftDivisionCayleyTable` 5.2-2
`LeftInnerMapping` 6.5-1
`LeftInnerMappingGroup` 6.5-2
`LeftInverse` 5.3-1
`LeftMultiplicationGroup` 6.4-1
`LeftNucleus` 6.6-1
`LeftSection` 6.3-2
`LeftTranslation` 6.3-1
`LibraryLoop` 9.1-1
License .-2
loop 2.1
alternative 7.4
associated left Bruck 8.1-1
automorphic 7.7
C 7.4
Chein 8.2-3
code 7.8-1
conjugacy closed 7.6
extra 7.4
flexible 7.4
LC 7.4
left alternative 7.4
left automorphic 7.7
left Bol 3.3 7.4 8.1-1
left Bruck 7.8-3
left conjugacy closed 7.6
left K 7.8-3
left nuclear square 7.4
left power alternative 7.5
middle automorphic 7.7
middle nuclear square 7.4
Moufang 7.4
nilpotent 2.4 4.9-2
nuclear square 7.4
octonion 9.4-1
of Bol-Moufang type 7.4
Osborn 7.6-4
Paige 9.9
power alternative 7.5
power associative 5.1-5
RC 7.4
right alternative 7.4
right automorphic 7.7
right Bol 7.4
right Bruck 7.8-4
right conjugacy closed 7.6
right K 7.8-4
right nuclear square 7.4
right power alternative 7.5
sedenion 9.12
simple 3.3 6.7-3
solvable 2.4
Steiner 7.8-2
strongly nilpotent 6.9-3
loop isotope, principal 2.6
loop table 4.1
`LoopByCayleyTable` 4.4-1
`LoopByCyclicModification` 8.2-1
`LoopByDihedralModification` 8.2-2
`LoopByExtension` 4.8-2
`LoopByLeftSection` 4.6-2
`LoopByRightFolder` 4.7-1
`LoopByRightSection` 4.6-3
`LoopFromFile` 4.5-1
`LoopIsomorph` 6.11-7
`LoopMG2` 8.2-3
`LoopsUpToIsomorphism` 6.11-4
`LoopsUpToIsotopism` 6.12-2
`LowerCentralSeries` 6.9-5
magma 2.1
medial quasigroup 7.3-7
`MiddleInnerMapping` 6.5-1
`MiddleInnerMappingGroup` 6.5-2
`MiddleNucleus` 6.6-1
modification, cyclic 8.2-1
dihedral 8.2-2
Moufang 8.2
Moufang loop 7.4
`MoufangLoop` 9.4-1
multiplication group 2.2
left 2.2
relative 6.4-2
relative left 6.4-2
relative right 6.4-2
right 2.2
multiplication table 4.1
`MultiplicationGroup` 6.4-1
`MyLibraryLoop` 9.1-2
`NaturalHomomorphismByNormalSubloop` 6.8-2
neutral element 2.1
nilpotence class 2.4
`NilpotencyClassOfLoop` 6.9-2
nilpotent loop 2.4
strongly 6.9-3
`NilpotentLoop` 9.10-1
normal closure 6.7-2
normal subloop 6.7-1
`NormalClosure` 6.7-2
`NormalizedQuasigroupTable` 4.3-3
`Nuc` 6.6-2
nuclear square loop 7.4
left 7.4
middle 7.4
right 7.4
`NuclearExtension` 4.8-1
nucleus 2.3
left 2.3
middle 2.3
right 2.3
`NucleusOfLoop` 6.6-2
`NucleusOfQuasigroup` 6.6-2
octonion loop 9.4-1
`One` 5.1-3
`OneLoopTableInGroup` 8.4-3
`OneLoopWithMltGroup` 8.4-6
`OneProperLoopTableInGroup` 8.4-4
`Opposite` 4.12-1
opposite quasigroup 4.12
`OppositeLoop` 4.12-1
`OppositeQuasigroup` 4.12-1
Osborn loop 7.6-4
Paige loop 9.9
`PaigeLoop` 9.9-1
`Parent` 6.1-1
`PosInParent` 6.1-3
`Position` 6.1-2
power alternative loop 7.5
left 7.5
right 7.5
power associative loop 5.1-5
power associative quasigroup 7.1-3
`PrincipalLoopIsotope` 4.10-2
quasigroup 2.1
diassociative 7.1-4
distributive 7.3-6
entropic 7.3-7
idempotent 7.3-3
left distributive 7.3-6
medial 7.3-7
opposite 4.12
power associative 7.1-3
right distributive 7.3-6
semisymmetric 7.3-1
Steiner 7.3-4
totally symmetric 7.3-2
unipotent 7.3-5
quasigroup table 4.1
`QuasigroupByCayleyTable` 4.4-1
`QuasigroupByLeftSection` 4.6-2
`QuasigroupByRightFolder` 4.7-1
`QuasigroupByRightSection` 4.6-3
`QuasigroupFromFile` 4.5-1
`QuasigroupIsomorph` 6.11-6
`QuasigroupsUpToIsomorphism` 6.11-3
`RandomLoop` 4.9-1
`RandomNilpotentLoop` 4.9-2
`RandomQuasigroup` 4.9-1
RC loop 7.4
`RCCLoop` 9.7-1
`RelativeLeftMultiplicationGroup` 6.4-2
`RelativeMultiplicationGroup` 6.4-2
`RelativeRightMultiplicationGroup` 6.4-2
`RightBolLoop` 9.2-2
`RightBolLoopByExactGroupFactorization` 8.1-3
`RightBruckLoop` 9.3-2
`RightConjugacyClosedLoop` 9.7-1
`RightCosets` 6.2-6
`RightDivision` 5.2-1 5.2-1 5.2-1
`RightDivisionCayleyTable` 5.2-2
`RightInnerMapping` 6.5-1
`RightInnerMappingGroup` 6.5-2
`RightInverse` 5.3-1
`RightMultiplicationGroup` 6.4-1
`RightNucleus` 6.6-1
`RightSection` 6.3-2
`RightTranslation` 6.3-1
`RightTransversal` 6.2-7
section, left 2.2
right 2.2
sedenion loop 9.12
semisymmetric quasigroup 7.3-1
`SetLoopElmName` 3.4-1
`SetQuasigroupElmName` 3.4-1
simple loop 3.3 6.7-3
`Size` 5.1-4
`SmallGeneratingSet` 5.5-3
`SmallLoop` 9.8-1
solvability class 2.4
solvable loop 2.4
Steiner loop 7.8-2
Steiner quasigroup 7.3-4
`SteinerLoop` 9.6-1
strongly nilpotent loop 6.9-3
subloop 2.3
`Subloop` 6.2-2
subloop, normal 2.3 6.7-1
subquasigroup 2.3
`Subquasigroup` 6.2-1
totally symmetric quasigroup 7.3-2
translation, left 2.2
right 2.2
transversal 6.2-7
`TrialityPcGroup` 8.3-2
`TrialityPermGroup` 8.3-1
unipotent quasigroup 7.3-5
`UpperCentralSeries` 6.9-4

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