loops : a GAP 4 package - Index
A
B
C
D
E
F
G
H
I
L
M
N
O
P
Q
R
S
T
U
W
- A typical library 8.1
- About Cayley tables 4.1
- Additional varieties of loops 6.6
- antiautomorphic inverse property 6.2
- AreEqualDiscriminators 5.13.2
- AsGroup 4.6.4
- AsLoop 4.6.2
- AsQuasigroup 4.6.1
- Associativity, commutativity and generalizations 6.1
- Associator 4.12.1
- associator 4.12
- associator subloop 5.7
- Associators and commutators 4.12
- AssociatorSubloop 5.7.6
- automorphic inverse property 6.2
- AutomorphismGroup 5.12.2
- Basic arithmetic operations 4.10
- Basic attributes 4.9
- Basic methods and attributes 4.0
- C-loops 6.4
- Calculating with quasigroups 3.3
- Canonical and normalized Cayley tables 4.3
- CanonicalCayleyTable 4.3.1
- Cayley table 4.1
- CayleyTable 4.9.2
- CC-loops 8.5
- CCLoop 8.5.1
- Center 5.7.5
- Commutant 5.7.4
- commutant 5.7
- Commutator 4.12.1
- commutator 4.12
- Comparing quasigroups with common parent 5.2
- Conjugacy closed loops and related properties 6.5
- Conversions 4.6
- Conversions between magmas, quasigroups, loops and groups 3.2
- Creating quasigroups and loops from a file 4.5
- Creating quasigroups and loops manually 4.4
- cyclic modification 7.1
- DerivedLength 5.11.1
- DerivedSubloop 5.11.1
- dihedral modification 7.1
- DirectProduct 4.7.1
- Discriminator 5.13.1
- DisplayLibraryInfo 8.1.3
- distributive quasigroup 6.3
- Documentation 1.2
- Elements 4.9.1
- Exponent 4.9.6
- exponent 4.9
- extra loops 6.4
- Factor loops 5.9
- FactorLoop 5.9.1
- Feedback 1.4
- Files A.0
- Filters built into the package B.0
- flexible loops 6.4
- FrattinifactorSize 5.11.1
- FrattiniSubloop 5.11.1
- Generators 4.13
- GeneratorsOfLoop 4.13.1
- GeneratorsOfQuasigroup 4.13.1
- GeneratorsSmallest 4.13.2
- group 2.1
- group with triality 7.2
- groupoid 2.1
- HasAntiautomorphicInverseProperty 6.2.3
- HasAutomorphicInverseProperty 6.2.3
- HasInverseProperty 6.2.1
- HasLeftInverseProperty 6.2.1
- HasRightInverseProperty 6.2.1
- HasTwosidedInverses 6.2.1
- HasWeakInverseProperty 6.2.2
- homomorphism 2.3
- Homomorphisms and homotopisms 2.3
- homotopism 2.3
- How are isomorphisms computed 5.13
- How the package works 3.0
- identity element 2.1
- identity of Bol-Moufang type 6.4
- inner mapping group 5.6
- Inner mapping groups 5.6
- InnerMappingGroup 5.6.1
- Installation 1.1
- Interesting loops 8.7
- InterestingLoop 8.7.1
- Introduction 1.0
- Inverse 4.11.1
- inverse 4.11
- Inverse properties 6.2
- inverse property 6.2
- IsAlternative 6.4.1
- IsAssociative 6.1.1
- IsCCLoop 6.5.1
- IsCLoop 6.4.1
- IsCommutative 6.1.1
- IsDiassociative 6.1.2
- IsDistributive 6.3.3
- IsEntropic 6.3.3
- IsExtraLoop 6.4.1
- IsFlexible 6.4.1
- IsIdempotent 6.3.2
- IsLCCLoop 6.5.1
- IsLCLoop 6.4.1
- IsLDistributive 6.3.4
- IsLeftAlternative 6.4.1
- IsLeftBolLoop 6.4.1
- IsLeftBruckLoop 6.6.1
- IsLeftDistributive 6.3.3
- IsLeftKLoop 6.6.1
- IsLeftNuclearSquareLoop 6.4.1
- IsLoopCayleyTable 4.2.2
- IsLoopTable 4.2.2
- IsMedial 6.3.3
- IsMiddleNuclearSquareLoop 6.4.1
- IsMoufangLoop 6.4.1
- IsNilpotent 5.10.1
- IsNormal 5.8.1
- IsNuclearSquareLoop 6.4.1
- isomorphism 2.3
- IsomorphismLoops 5.12.1
- Isomorphisms and automorphisms 5.12
- IsomorphismTypeOfMoufangLoop 8.3.2
- IsOsbornLoop 6.5.2
- isotopism 2.3
- IsPowerAssociative 6.1.2
- IsQuasigroupCayleyTable 4.2.1
- IsQuasigroupTable 4.2.1
- IsRCCLoop 6.5.1
- IsRCLoop 6.4.1
- IsRDistributive 6.3.4
- IsRightAlternative 6.4.1
- IsRightBolLoop 6.4.1
- IsRightBruckLoop 6.6.1
- IsRightDistributive 6.3.3
- IsRightKLoop 6.6.1
- IsRightNuclearSquareLoop 6.4.1
- IsSemisymmetric 6.3.1
- IsSimple 5.8.3
- IsSolvable 5.11.1
- IsSteinerLoop 6.6.2
- IsSteinerQuasigroup 6.3.2
- IsStronglyNilpotent 5.10.2
- IsSubloop 5.3.2
- IsSubquasigroup 5.3.2
- IsTotallySymmetric 6.3.1
- IsUnipotent 6.3.2
- iterated centers 5.10
- Latin square 4.1
- LC-loops 6.4
- left alternative loops 6.4
- Left Bol loops 8.2
- left Bol loops 6.4
- left division 4.10
- left inner mapping group 5.6
- left inverse 4.11
- left inverse property 6.2
- left multiplication group 2.2
- left nuclear square loops 6.4
- left nucleus 5.7
- left section 2.2
- left translation 2.2
- LeftBolLoop 8.2.1
- LeftDivision 4.10.2
- LeftInnerMappingGroup 5.6.1
- LeftInverse 4.11.1
- LeftMultiplicationGroup 5.5.1
- LeftNucleus 5.7.1
- LeftSection 5.4.2
- LeftTranslation 5.4.1
- Libraries of small loops 8.0
- LibraryLoop 8.1.2
- list of files A.0
- loop 2.1
- loop table 4.1
- LoopByCayleyTable 4.4.2
- LoopByCyclicModification 7.1.1
- LoopByDihedralModification 7.1.2
- LoopFromFile 4.5.1
- LoopMG2 7.1.3
- Loops of Bol-Moufang type and related properties 6.4
- lower central series 5.10
- LowerCentralSeries 5.10.4
- magma 2.1
- Mathematical background 2.0
- middle nuclear square loops 6.4
- middle nucleus 5.7
- MiddleNucleus 5.7.1
- monoid 2.1
- Moufang center 5.7
- Moufang loops 6.4
- Moufang modifications 7.1
- MoufangLoop 8.3.1
- multiplication group 2.2
- Multiplication groups 5.5
- multiplication table 4.1
- MultiplicationGroup 5.5.1
- MultiplicativeNeutralElement 4.9.4
- MyLibraryLoop 8.1.1
- Naming, viewing and printing quasigroups and their elements 3.4
- NaturalHomomorphismByNormalSubloop 5.9.2
- neutral element 2.1
- Nilpotency and central series 5.10
- NilpotencyClassOfLoop 5.10.1
- normal closure 5.8
- Normal subloops 5.8
- NormalClosure 5.8.2
- NormalizedQuasigroupTable 4.3.2
- Nuc 5.7.1
- Nuclei, commutant, center, and associator subloop 5.7
- nucleus 5.7
- NucleusOfLoop 5.7.2
- NucleusOfQuasigroup 5.7.3
- octonion loop 8.3
- octonions 8.3
- One 4.9.3
- Opposite 4.8.1
- opposite quasigroup 4.8
- Opposite quasigroups and loops 4.8
- Paige loops 8.6
- PaigeLoop 8.6.1
- Parent 5.1.1
- Parent of a quasigroup 5.1
- PosInParent 5.1.3
- Position 5.1.2
- power-associative 4.11
- power-associative loop 4.9
- Powers and inverses 4.11
- principal isotopism 2.3
- principal loop isotope 2.3
- PrincipalLoopIsotope 4.6.3
- Products of loops 4.7
- quasigroup 2.1
- quasigroup table 4.1
- QuasigroupByCayleyTable 4.4.1
- QuasigroupFromFile 4.5.1
- Quasigroups and loops 2.1
- RC-loops 6.4
- relative left multiplication group 5.5
- relative multiplication group 5.5
- relative right multiplication group 5.5
- RelativeLeftMultiplicationGroup 5.5.2
- RelativeMultiplicationGroup 5.5.2
- RelativeRightMultiplicationGroup 5.5.2
- Representing quasigroups 3.1
- right alternative loops 6.4
- right Bol loops 6.4
- right division 4.10
- right inner mapping group 5.6
- right inverse 4.11
- right inverse property 6.2
- right multiplication group 2.2
- right nuclear square loops 6.4
- right nucleus 5.7
- right section 2.2
- right translation 2.2
- RightDivision 4.10.2
- RightInnerMappingGroup 5.6.1
- RightInverse 4.11.1
- RightMultiplicationGroup 5.5.1
- RightNucleus 5.7.1
- RightSection 5.4.2
- RightTranslation 5.4.1
- semigroup 2.1
- SetLoopElmName 3.4.1
- SetQuasigroupElmName 3.4.1
- Size 4.9.5
- Small Moufang loops 8.3
- Solvability 5.11
- Some methods based on permutation groups 5.0
- Some properties of quasigroups 6.3
- Specific methods 7.0
- Steiner loop 6.6
- Steiner loops 8.4
- SteinerLoop 8.4.1
- Subloop 5.3.1
- Subquasigroup 5.3.1
- Subquasigroups and subloops 5.3
- Test files 1.3
- Testing Cayley tables 4.2
- Testing properties of quasigroups and loops 6.0
- Translations 2.2
- Translations and sections 5.4
- Triality for Moufang loops 7.2
- TrialityPcGroup 7.2.2
- TrialityPermGroup 7.2.1
- two-sided inverse 2.1
- two-sided inverses 6.2
- upper central series 5.10
- UpperCentralSeries 5.10.3
- weak inverse property 6.2
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loops manual
szeptember 2005