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