loops/doc/chapInd.txt

  
  
  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
  alternative loop, left  7.4
  alternative loop, right  7.4
  antiautomorphic inverse property  7.2-5
  AreEqualDiscriminators  6.11-9
  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
  automorphic loop, left  7.7
  automorphic loop, middle  7.7
  automorphic loop, right  7.7
  AutomorphicLoop  9.10-1
  AutomorphismGroup  6.11-5
  Bol loop, left  3.3
  Bol loop, left  7.4
  Bol loop, left  8.1-1
  Bol loop, right  7.4
  Bruck loop, associated left  8.1-1
  Bruck loop, left  7.8-3
  Bruck loop, right  7.8-4
  C loop  7.4
  CanonicalCayleyTable  4.3-1
  CanonicalCopy  4.3-2
  Cayley table  4.1
  Cayley table, canonical  4.3-1
  CayleyTable  5.1-2
  CayleyTableByPerms  4.6-1
  CCLoop  9.6-3
  center  2.3
  Center  6.6-4
  central series, lower  6.9-5
  central series, upper  2.4
  Chein loop  8.2-3
  cocycle  4.8
  code loop  7.8-1
  CodeLoop  9.4-1
  commutant  2.3
  Commutant  6.6-3
  commutator  2.5
  Commutator  5.4-2
  conjugacy closed loop  7.6
  conjugacy closed loop, left  7.6
  conjugacy closed loop, right  7.6
  ConjugacyClosedLoop  9.6-3
  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  6.11-8
  DisplayLibraryInfo  9.1-3
  distributive quasigroup  7.3-6
  distributive quasigroup, left  7.3-6
  distributive quasigroup, right  7.3-6
  division, left  2.2
  division, 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
  extension, 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
  identity, of Bol-Moufang type  7.4
  inner mapping, left  6.5
  inner mapping, middle  6.5
  inner mapping, right  6.5
  inner mapping group  2.2
  inner mapping group, left  2.2
  inner mapping group, middle  6.5
  inner mapping group, right  2.2
  InnerMappingGroup  6.5-3
  InterestingLoop  9.11-1
  IntoGroup  4.10-4
  IntoLoop  4.10-3
  IntoQuasigroup  4.10-1
  inverse  5.3
  Inverse  5.3-1
  inverse, left  5.3
  inverse, left  7.2
  inverse, right  5.3
  inverse, right  7.2
  inverse, two-sided  2.1
  inverse, two-sided  7.2-2
  inverse property  7.2-1
  inverse property, antiautomorphic  7.2-5
  inverse property, automorphic  7.2-4
  inverse property, left  7.2-1
  inverse property, right  7.2-1
  inverse property, 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  6.11-7
  IsomorphicCopyByPerm  6.11-6
  isomorphism  2.6
  IsomorphismLoops  6.11-2
  IsomorphismQuasigroups  6.11-1
  IsOsbornLoop  7.6-4
  isotopism  2.6
  isotopism, 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  9.12-1
  K loop, left  7.8-3
  K loop, right  7.8-4
  latin square  2.1
  latin square  4.1
  latin square, random  4.9
  LC loop  7.4
  LCCLoop  9.6-2
  LeftBolLoop  9.2-1
  LeftConjugacyClosedLoop  9.6-2
  LeftDivision  5.2-1
  LeftDivision  5.2-1
  LeftDivision  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
  loop  2.1
  loop, C  7.4
  loop, Chein  8.2-3
  loop, LC  7.4
  loop, Moufang  7.4
  loop, Osborn  7.6-4
  loop, Paige  9.8
  loop, RC  7.4
  loop, Steiner  7.8-2
  loop, alternative  7.4
  loop, associated left Bruck  8.1-1
  loop, automorphic  7.7
  loop, code  7.8-1
  loop, conjugacy closed  7.6
  loop, extra  7.4
  loop, flexible  7.4
  loop, left Bol  3.3
  loop, left Bol  7.4
  loop, left Bol  8.1-1
  loop, left Bruck  7.8-3
  loop, left K  7.8-3
  loop, left alternative  7.4
  loop, left automorphic  7.7
  loop, left conjugacy closed  7.6
  loop, left nuclear square  7.4
  loop, left power alternative  7.5
  loop, middle automorphic  7.7
  loop, middle nuclear square  7.4
  loop, nilpotent  2.4
  loop, nilpotent  4.9-2
  loop, nuclear square  7.4
  loop, octonion  9.3-1
  loop, of Bol-Moufang type  7.4
  loop, power alternative  7.5
  loop, power associative  5.1-5
  loop, right Bol  7.4
  loop, right Bruck  7.8-4
  loop, right K  7.8-4
  loop, right alternative  7.4
  loop, right automorphic  7.7
  loop, right conjugacy closed  7.6
  loop, right nuclear square  7.4
  loop, right power alternative  7.5
  loop, sedenion  9.11
  loop, simple  3.3
  loop, simple  6.7-3
  loop, solvable  2.4
  loop, 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
  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, Moufang  8.2
  modification, cyclic  8.2-1
  modification, dihedral  8.2-2
  Moufang loop  7.4
  MoufangLoop  9.3-1
  multiplication group  2.2
  multiplication group, left  2.2
  multiplication group, relative  6.4-2
  multiplication group, relative left  6.4-2
  multiplication group, relative right   6.4-2
  multiplication group, 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
  nilpotent loop, strongly  6.9-3
  NilpotentLoop  9.9-1
  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
  nuclear square loop, left  7.4
  nuclear square loop, middle  7.4
  nuclear square loop, right  7.4
  NuclearExtension  4.8-1
  nucleus  2.3
  nucleus, left  2.3
  nucleus, middle  2.3
  nucleus, right  2.3
  NucleusOfLoop  6.6-2
  NucleusOfQuasigroup  6.6-2
  octonion loop  9.3-1
  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  9.8
  PaigeLoop  9.8-1
  Parent  6.1-1
  PosInParent  6.1-3
  Position  6.1-2
  power alternative loop  7.5
  power alternative loop, left  7.5
  power alternative loop, right  7.5
  power associative loop  5.1-5
  power associative quasigroup  7.1-3
  PrincipalLoopIsotope  4.10-2
  quasigroup  2.1
  quasigroup, Steiner  7.3-4
  quasigroup, diassociative  7.1-4
  quasigroup, distributive  7.3-6
  quasigroup, entropic  7.3-7
  quasigroup, idempotent  7.3-3
  quasigroup, left distributive  7.3-6
  quasigroup, medial  7.3-7
  quasigroup, opposite  4.12
  quasigroup, power associative  7.1-3
  quasigroup, right distributive  7.3-6
  quasigroup, semisymmetric  7.3-1
  quasigroup, totally symmetric  7.3-2
  quasigroup, 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
  QuasigroupsUpToIsomorphism  6.11-3
  RandomLoop  4.9-1
  RandomNilpotentLoop  4.9-2
  RandomQuasigroup  4.9-1
  RC loop  7.4
  RCCLoop  9.6-1
  RelativeLeftMultiplicationGroup  6.4-2
  RelativeMultiplicationGroup  6.4-2
  RelativeRightMultiplicationGroup  6.4-2
  RightBolLoop  9.2-2
  RightBolLoopByExactGroupFactorization  8.1-3
  RightConjugacyClosedLoop  9.6-1
  RightCosets  6.2-6
  RightDivision  5.2-1
  RightDivision  5.2-1
  RightDivision  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
  section, right  2.2
  sedenion loop  9.11
  semisymmetric quasigroup  7.3-1
  SetLoopElmName  3.4-1
  SetQuasigroupElmName  3.4-1
  simple loop  3.3
  simple loop  6.7-3
  Size  5.1-4
  SmallGeneratingSet  5.5-3
  SmallLoop  9.7-1
  solvability class  2.4
  solvable loop  2.4
  Steiner loop  7.8-2
  Steiner quasigroup  7.3-4
  SteinerLoop  9.5-1
  strongly nilpotent loop  6.9-3
  subloop  2.3
  Subloop  6.2-2
  subloop, normal  2.3
  subloop, normal  6.7-1
  subquasigroup  2.3
  Subquasigroup  6.2-1
  totally symmetric quasigroup  7.3-2
  translation, left  2.2
  translation, right  2.2
  transversal  6.2-7
  TrialityPcGroup  8.3-2
  TrialityPermGroup  8.3-1
  unipotent quasigroup  7.3-5
  UpperCentralSeries  6.9-4
  
  
  -------------------------------------------------------