\letter A
  About Cayley tables, \indexit{11}
  Additional varieties of loops, \indexit{25}
  alternative loop, 23
  antiautomorphic inverse property, 22
  `AreEqualDiscriminators', 21
  `AsGroup', 13
  `AsLoop', 8, 12
  `AsQuasigroup', 8, 12
  Associativity, commutativity and generalizations, \indexit{22}
  `Associator', 15
  associator, 15
  Associators and commutators, \indexit{15}
  `AssociatorSubloop', 20
  associator subloop, 19
  A typical library, \indexit{28}
  automorphic inverse property, 22
  `AutomorphismGroup', 21
\letter B
  Basic arithmetic operations, \indexit{14}
  Basic attributes, \indexit{13}
\letter C
  c-loops, 23
  Calculating with quasigroups, \indexit{9}
  Canonical and normalized Cayley tables, \indexit{11}
  `CanonicalCayleyTable', 11
  `CayleyTable', 13
  cayley table, 11
  CC-loops, \indexit{29}
  `CCLoop', 30
  `Center', 19
  `Commutant', 19
  commutant, 19
  `Commutator', 15
  commutator, 15
  Comparing quasigroups with common parent, \indexit{17}
  conjugacy closed loop, 24, 29
  Conjugacy closed loops and related properties, \indexit{24}
  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, 26
\letter D
  `DerivedLength', 21
  `DerivedSubloop', 21
  diassociative loop, 22
  dihedral modification, 26
  `DirectProduct', 13
  `Discriminator', 21
  `DisplayLibraryInfo', 28
  distributive quasigroup, 23
  Documentation, \indexit{5}
\letter E
  `Elements', 13
  entropic quasigroup, 23
  `Exponent', 14
  exponent, 14
  extra loops, 23
\letter F
  `FactorLoop', 20
  Factor loops, \indexit{20}
  Feedback, \indexit{5}
  flexible loops, 23
  `FrattinifactorSize', 21
  `FrattiniSubloop', 21
\letter G
  Generators, \indexit{15}
  `GeneratorsOfLoop', 15
  `GeneratorsOfQuasigroup', 15
  `GeneratorsSmallest', 15
  group, 6
  groupoid, 6
  group with triality, 26
\letter H
  `HasAntiautomorphicInverseProperty', 22
  `HasAutomorphicInverseProperty', 22
  `HasInverseProperty', 22
  `HasLeftInverseProperty', 22
  `HasRightInverseProperty', 22
  `HasTwosidedInverses', 22
  `HasWeakInverseProperty', 22
  homomorphism, 6
  Homomorphisms and homotopisms, \indexit{6}
  homotopism, 6
  How are isomorphisms computed, \indexit{21}
\letter I
  idempotent quasigroup, 23
  identity element, 6
  identity of bol-moufang type, 23
  `InnerMappingGroup', 19
  inner mapping group, 19
  Inner mapping groups, \indexit{19}
  Installation, \indexit{5}
  `InterestingLoop', 30
  Interesting loops, \indexit{30}
  `Inverse', 15
  inverse, 15
  Inverse properties, \indexit{22}
  inverse property, 22
  `IsAlternative', 24
  `IsAssociative', 22
  `IsCCLoop', 24
  `IsCLoop', 24
  `IsCommutative', 22
  `IsDiassociative', 22
  `IsDistributive', 23
  `IsEntropic', 23
  `IsExtraLoop', 24
  `IsFlexible', 24
  `IsIdempotent', 23
  `IsLCCLoop', 24
  `IsLCLoop', 24
  `IsLDistributive', 23
  `IsLeftAlternative', 24
  `IsLeftBolLoop', 24
  `IsLeftBruckLoop', 25
  `IsLeftDistributive', 23
  `IsLeftKLoop', 25
  `IsLeftNuclearSquareLoop', 24
  `IsLeftPowerAlternative', 24
  `IsLoopCayleyTable', 11
  `IsLoopTable', 11
  `IsMedial', 23
  `IsMiddleNuclearSquareLoop', 24
  `IsMoufangLoop', 24
  `IsNilpotent', 20
  `IsNormal', 20
  `IsNuclearSquareLoop', 24
  isomorphism, 6
  `IsomorphismLoops', 21
  Isomorphisms and automorphisms, \indexit{21}
  `IsomorphismTypeOfMoufangLoop', 29
  `IsOsbornLoop', 25
  isotopism, 6
  `IsPowerAlternative', 24
  `IsPowerAssociative', 22
  `IsQuasigroupCayleyTable', 11
  `IsQuasigroupTable', 11
  `IsRCCLoop', 24
  `IsRCLoop', 24
  `IsRDistributive', 23
  `IsRightAlternative', 24
  `IsRightBolLoop', 24
  `IsRightBruckLoop', 25
  `IsRightDistributive', 23
  `IsRightKLoop', 25
  `IsRightNuclearSquareLoop', 24
  `IsRightPowerAlternative', 24
  `IsSemisymmetric', 23
  `IsSimple', 20
  `IsSolvable', 21
  `IsSteinerLoop', 25
  `IsSteinerQuasigroup', 23
  `IsStronglyNilpotent', 20
  `IsSubloop', 17
  `IsSubquasigroup', 17
  `IsTotallySymmetric', 23
  `IsUnipotent', 23
  iterated centers, 20
\letter K
  k-loop, 25
\letter L
  latin square, 6, 11
  lc-loops, 23
  left alternative loops, 23
  `LeftBolLoop', 28
  Left Bol loops, \indexit{28}
  left bol loops, 23
  left bruck loop, 25
  left conjugacy closed loop, 24
  left distributive quasigroup, 23
  `LeftDivision', 14
  left division, 14
  `LeftDivisionCayleyTable', 15
  `LeftInnerMappingGroup', 19
  left inner mapping group, 19
  `LeftInverse', 15
  left inverse, 15
  left inverse property, 22
  `LeftMultiplicationGroup', 18
  left multiplication group, 6
  left nuclear square loops, 23
  `LeftNucleus', 19
  left nucleus, 19
  left power alternative loop, 24
  `LeftSection', 18
  left section, 6
  `LeftTranslation', 18
  left translation, 6
  `LibraryLoop', 28
  list of files, 31
  loop, 6
  `LoopByCayleyTable', 12
  `LoopByCyclicModification', 26
  `LoopByDihedralModification', 26
  `LoopFromFile', 12
  `LoopMG2', 26
  Loops of Bol-Moufang type, \indexit{23}
  loops of bol-moufang type, 23
  loop table, 11
  `LowerCentralSeries', 20
  lower central series, 20
\letter M
  magma, 6
  medial quasigroup, 23
  middle nuclear square loops, 23
  `MiddleNucleus', 19
  middle nucleus, 19
  monoid, 6
  moufang center, 19
  `MoufangLoop', 28
  moufang loops, 23
  Moufang modifications, \indexit{26}
  moufang modifications, 26
  `MultiplicationGroup', 18
  multiplication group, 6
  Multiplication groups, \indexit{18}
  multiplication table, 11
  `MultiplicativeNeutralElement', 13
  `MyLibraryLoop', 28
\letter N
  Naming, viewing and printing quasigroups and their elements, \indexit{9}
  `NaturalHomomorphismByNormalSubloop', 20
  neutral element, 6
  Nilpotency and central series, \indexit{20}
  `NilpotencyClassOfLoop', 20
  `NormalClosure', 20
  normal closure, 20
  `NormalizedQuasigroupTable', 11
  normal subloop, 20
  Normal subloops, \indexit{20}
  `Nuc', 19
  nuclear square loop, 23
  Nuclei, commutant, center, and associator subloop, \indexit{19}
  nucleus, 19
  `NucleusOfLoop', 19
  `NucleusOfQuasigroup', 19
\letter O
  octonion loop, 29
  octonions, 29
  `One', 13
  `Opposite', 13
  opposite quasigroup, 13
  Opposite quasigroups and loops, \indexit{13}
  osborn loop, 25
\letter P
  `PaigeLoop', 30
  paige loop, 30
  Paige loops, \indexit{30}
  `Parent', 17
  Parent of a quasigroup, \indexit{17}
  `PosInParent', 17
  `Position', 17
  power-associative, 15
  power-associative loop, 14, 22
  power alternative loop, 24
  Power alternative loops, \indexit{24}
  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, 23
  `RelativeLeftMultiplicationGroup', 19
  relative left multiplication group, 18
  `RelativeMultiplicationGroup', 19
  relative multiplication group, 18
  `RelativeRightMultiplicationGroup', 19
  relative right multiplication group, 18
  Representing quasigroups, \indexit{8}
  right alternative loops, 23
  right bol loops, 23
  right bruck loop, 25
  right conjugacy closed loop, 24
  right distributive quasigroup, 23
  `RightDivision', 14
  right division, 14
  `RightDivisionCayleyTable', 15
  `RightInnerMappingGroup', 19
  right inner mapping group, 19
  `RightInverse', 15
  right inverse, 15
  right inverse property, 22
  `RightMultiplicationGroup', 18
  right multiplication group, 6
  right nuclear square loops, 23
  `RightNucleus', 19
  right nucleus, 19
  right power alternative loop, 24
  `RightSection', 18
  right section, 6
  `RightTranslation', 18
  right translation, 6
\letter S
  sedenions, 30
  semigroup, 6
  semisymmetric quasigroup, 22
  `SetLoopElmName', 10
  `SetQuasigroupElmName', 10
  simple loop, 20
  `Size', 14
  Small Moufang loops, \indexit{28}
  Solvability, \indexit{21}
  Some properties of quasigroups, \indexit{22}
  `SteinerLoop', 29
  steiner loop, 25
  Steiner loops, \indexit{29}
  steiner quasigroup, 23
  strongly nilpotent loop, 20
  `Subloop', 17
  `Subquasigroup', 17
  Subquasigroups and subloops, \indexit{17}
\letter T
  Test files, \indexit{5}
  Testing Cayley tables, \indexit{11}
  totally symmetric quasigroup, 22
  Translations, \indexit{6}
  Translations and sections, \indexit{18}
  Triality for Moufang loops, \indexit{26}
  `TrialityPcGroup', 27
  `TrialityPermGroup', 26
  two-sided inverse, 6
  two-sided inverses, 22
\letter U
  unipotent quasigroup, 23
  `UpperCentralSeries', 20
  upper central series, 20
\letter W
  weak inverse property, 22
