\letter A
  About Cayley tables, \indexit{11}
  Additional varieties of loops, \indexit{23}
  alternative loop, 22
  antiautomorphic inverse property, 21
  `AreEqualDiscriminators', 20
  `AsGroup', 13
  `AsLoop', 8, 12
  `AsQuasigroup', 8, 12
  Associativity, commutativity and generalizations, \indexit{21}
  `Associator', 15
  associator, 15
  Associators and commutators, \indexit{15}
  `AssociatorSubloop', 19
  associator subloop, 18
  A typical library, \indexit{27}
  automorphic inverse property, 21
  `AutomorphismGroup', 20
\letter B
  Basic arithmetic operations, \indexit{14}
  Basic attributes, \indexit{13}
\letter C
  c-loops, 22
  Calculating with quasigroups, \indexit{9}
  Canonical and normalized Cayley tables, \indexit{11}
  `CanonicalCayleyTable', 11
  `CayleyTable', 13
  cayley table, 11
  CC-loops, \indexit{28}
  `CCLoop', 29
  `Center', 18
  `Commutant', 18
  commutant, 18
  `Commutator', 15
  commutator, 15
  Comparing quasigroups with common parent, \indexit{16}
  conjugacy closed loop, 23, 28
  Conjugacy closed loops and related properties, \indexit{23}
  Conversions, \indexit{12}
  Conversions between magmas, quasigroups, loops and groups, \indexit{8}
  Creating quasigroups and loops from a file, \indexit{12}
  Creating quasigroups and loops manually, \indexit{11}
  cyclic modification, 25
\letter D
  `DerivedLength', 20
  `DerivedSubloop', 20
  diassociative loop, 21
  dihedral modification, 25
  `DirectProduct', 13
  `Discriminator', 20
  `DisplayLibraryInfo', 27
  distributive quasigroup, 22
  Documentation, \indexit{5}
\letter E
  `Elements', 13
  entropic quasigroup, 22
  `Exponent', 14
  exponent, 14
  extra loops, 22
\letter F
  `FactorLoop', 19
  Factor loops, \indexit{19}
  Feedback, \indexit{5}
  flexible loops, 22
  `FrattinifactorSize', 20
  `FrattiniSubloop', 20
\letter G
  Generators, \indexit{15}
  `GeneratorsOfLoop', 15
  `GeneratorsOfQuasigroup', 15
  `GeneratorsSmallest', 15
  group, 6
  groupoid, 6
  group with triality, 25
\letter H
  `HasAntiautomorphicInverseProperty', 21
  `HasAutomorphicInverseProperty', 21
  `HasInverseProperty', 21
  `HasLeftInverseProperty', 21
  `HasRightInverseProperty', 21
  `HasTwosidedInverses', 21
  `HasWeakInverseProperty', 21
  homomorphism, 6
  Homomorphisms and homotopisms, \indexit{6}
  homotopism, 6
  How are isomorphisms computed, \indexit{20}
\letter I
  idempotent quasigroup, 22
  identity element, 6
  identity of bol-moufang type, 22
  `InnerMappingGroup', 18
  inner mapping group, 18
  Inner mapping groups, \indexit{18}
  Installation, \indexit{5}
  `InterestingLoop', 29
  Interesting loops, \indexit{29}
  `Inverse', 15
  inverse, 15
  Inverse properties, \indexit{21}
  inverse property, 21
  `IsAlternative', 23
  `IsAssociative', 21
  `IsCCLoop', 23
  `IsCLoop', 23
  `IsCommutative', 21
  `IsDiassociative', 21
  `IsDistributive', 22
  `IsEntropic', 22
  `IsExtraLoop', 23
  `IsFlexible', 23
  `IsIdempotent', 22
  `IsLCCLoop', 23
  `IsLCLoop', 23
  `IsLDistributive', 22
  `IsLeftAlternative', 23
  `IsLeftBolLoop', 23
  `IsLeftBruckLoop', 24
  `IsLeftDistributive', 22
  `IsLeftKLoop', 24
  `IsLeftNuclearSquareLoop', 23
  `IsLoopCayleyTable', 11
  `IsLoopTable', 11
  `IsMedial', 22
  `IsMiddleNuclearSquareLoop', 23
  `IsMoufangLoop', 23
  `IsNilpotent', 19
  `IsNormal', 19
  `IsNuclearSquareLoop', 23
  isomorphism, 6
  `IsomorphismLoops', 20
  Isomorphisms and automorphisms, \indexit{20}
  `IsomorphismTypeOfMoufangLoop', 28
  `IsOsbornLoop', 23
  isotopism, 6
  `IsPowerAssociative', 21
  `IsQuasigroupCayleyTable', 11
  `IsQuasigroupTable', 11
  `IsRCCLoop', 23
  `IsRCLoop', 23
  `IsRDistributive', 22
  `IsRightAlternative', 23
  `IsRightBolLoop', 23
  `IsRightBruckLoop', 24
  `IsRightDistributive', 22
  `IsRightKLoop', 24
  `IsRightNuclearSquareLoop', 23
  `IsSemisymmetric', 22
  `IsSimple', 19
  `IsSolvable', 20
  `IsSteinerLoop', 24
  `IsSteinerQuasigroup', 22
  `IsStronglyNilpotent', 19
  `IsSubloop', 16
  `IsSubquasigroup', 16
  `IsTotallySymmetric', 22
  `IsUnipotent', 22
  iterated centers, 19
\letter K
  k-loop, 23
\letter L
  latin square, 6, 11
  lc-loops, 22
  left alternative loops, 22
  `LeftBolLoop', 27
  Left Bol loops, \indexit{27}
  left bol loops, 22
  left bruck loop, 23
  left conjugacy closed loop, 23
  left distributive quasigroup, 22
  `LeftDivision', 14
  left division, 14
  `LeftInnerMappingGroup', 18
  left inner mapping group, 18
  `LeftInverse', 15
  left inverse, 15
  left inverse property, 21
  `LeftMultiplicationGroup', 17
  left multiplication group, 6
  left nuclear square loops, 22
  `LeftNucleus', 18
  left nucleus, 18
  `LeftSection', 17
  left section, 6
  `LeftTranslation', 17
  left translation, 6
  `LibraryLoop', 27
  list of files, 30
  loop, 6
  `LoopByCayleyTable', 12
  `LoopByCyclicModification', 25
  `LoopByDihedralModification', 25
  `LoopFromFile', 12
  `LoopMG2', 25
  loops of bol-moufang type, 22
  Loops of Bol-Moufang type and related properties, \indexit{22}
  loop table, 11
  `LowerCentralSeries', 19
  lower central series, 19
\letter M
  magma, 6
  medial quasigroup, 22
  middle nuclear square loops, 22
  `MiddleNucleus', 18
  middle nucleus, 18
  monoid, 6
  moufang center, 18
  `MoufangLoop', 27
  moufang loops, 22
  Moufang modifications, \indexit{25}
  moufang modifications, 25
  `MultiplicationGroup', 17
  multiplication group, 6
  Multiplication groups, \indexit{17}
  multiplication table, 11
  `MultiplicativeNeutralElement', 13
  `MyLibraryLoop', 27
\letter N
  Naming, viewing and printing quasigroups and their elements, \indexit{9}
  `NaturalHomomorphismByNormalSubloop', 19
  neutral element, 6
  Nilpotency and central series, \indexit{19}
  `NilpotencyClassOfLoop', 19
  `NormalClosure', 19
  normal closure, 19
  `NormalizedQuasigroupTable', 11
  normal subloop, 19
  Normal subloops, \indexit{19}
  `Nuc', 18
  nuclear square loop, 22
  Nuclei, commutant, center, and associator subloop, \indexit{18}
  nucleus, 18
  `NucleusOfLoop', 18
  `NucleusOfQuasigroup', 18
\letter O
  octonion loop, 28
  octonions, 28
  `One', 13
  `Opposite', 13
  opposite quasigroup, 13
  Opposite quasigroups and loops, \indexit{13}
  osborn loop, 23
\letter P
  `PaigeLoop', 29
  paige loop, 29
  Paige loops, \indexit{29}
  `Parent', 16
  Parent of a quasigroup, \indexit{16}
  `PosInParent', 16
  `Position', 16
  power-associative, 15
  power-associative loop, 14, 21
  Powers and inverses, \indexit{15}
  principal isotopism, 6
  `PrincipalLoopIsotope', 13
  principal loop isotope, 6
  Products of loops, \indexit{13}
\letter Q
  quasigroup, 6
  `QuasigroupByCayleyTable', 12
  `QuasigroupFromFile', 12
  Quasigroups and loops, \indexit{6}
  quasigroup table, 11
\letter R
  rc-loops, 22
  `RelativeLeftMultiplicationGroup', 18
  relative left multiplication group, 17
  `RelativeMultiplicationGroup', 18
  relative multiplication group, 17
  `RelativeRightMultiplicationGroup', 18
  relative right multiplication group, 17
  Representing quasigroups, \indexit{8}
  right alternative loops, 22
  right bol loops, 22
  right bruck loop, 23
  right conjugacy closed loop, 23
  right distributive quasigroup, 22
  `RightDivision', 14
  right division, 14
  `RightInnerMappingGroup', 18
  right inner mapping group, 18
  `RightInverse', 15
  right inverse, 15
  right inverse property, 21
  `RightMultiplicationGroup', 17
  right multiplication group, 6
  right nuclear square loops, 22
  `RightNucleus', 18
  right nucleus, 18
  `RightSection', 17
  right section, 6
  `RightTranslation', 17
  right translation, 6
\letter S
  sedenions, 29
  semigroup, 6
  semisymmetric quasigroup, 21
  `SetLoopElmName', 10
  `SetQuasigroupElmName', 10
  simple loop, 19
  `Size', 14
  Small Moufang loops, \indexit{27}
  Solvability, \indexit{19}
  Some properties of quasigroups, \indexit{21}
  `SteinerLoop', 28
  steiner loop, 24
  Steiner loops, \indexit{28}
  steiner quasigroup, 22
  strongly nilpotent loop, 19
  `Subloop', 16
  `Subquasigroup', 16
  Subquasigroups and subloops, \indexit{16}
\letter T
  Test files, \indexit{5}
  Testing Cayley tables, \indexit{11}
  totally symmetric quasigroup, 21
  Translations, \indexit{6}
  Translations and sections, \indexit{17}
  Triality for Moufang loops, \indexit{25}
  `TrialityPcGroup', 26
  `TrialityPermGroup', 25
  two-sided inverse, 6
  two-sided inverses, 21
\letter U
  unipotent quasigroup, 22
  `UpperCentralSeries', 19
  upper central series, 19
\letter W
  weak inverse property, 21
