\makelabel{loops:Introduction}{1}
\makelabel{loops:Installation}{1.1}
\makelabel{loops:Documentation}{1.2}
\makelabel{loops:Test files}{1.3}
\makelabel{loops:Feedback}{1.4}
\makelabel{loops:Acknowledgement}{1.5}
\makelabel{loops:Mathematical background}{2}
\makelabel{loops:Quasigroups and loops}{2.1}
\makelabel{loops:Translations}{2.2}
\makelabel{loops:Homomorphisms and homotopisms}{2.3}
\makelabel{loops:Extensions}{2.4}
\makelabel{loops:How the package works}{3}
\makelabel{loops:Representing quasigroups}{3.1}
\makelabel{loops:Conversions between magmas, quasigroups, loops and groups}{3.2}
\makelabel{loops:Calculating with quasigroups}{3.3}
\makelabel{loops:Naming, viewing and printing quasigroups and their elements}{3.4}
\makelabel{loops:SetQuasigroupElmName}{3.4.1}
\makelabel{loops:SetLoopElmName}{3.4.1}
\makelabel{loops:Creating quasigroups and loops}{4}
\makelabel{loops:About Cayley tables}{4.1}
\makelabel{loops:Testing Cayley tables}{4.2}
\makelabel{loops:IsQuasigroupTable}{4.2.1}
\makelabel{loops:IsQuasigroupCayleyTable}{4.2.1}
\makelabel{loops:IsLoopTable}{4.2.2}
\makelabel{loops:IsLoopCayleyTable}{4.2.2}
\makelabel{loops:Canonical and normalized Cayley tables}{4.3}
\makelabel{loops:CanonicalCayleyTable}{4.3.1}
\makelabel{loops:NormalizedQuasigroupTable}{4.3.2}
\makelabel{loops:Creating quasigroups and loops manually}{4.4}
\makelabel{loops:QuasigroupByCayleyTable}{4.4.1}
\makelabel{loops:LoopByCayleyTable}{4.4.2}
\makelabel{loops:Creating quasigroups and loops from a file}{4.5}
\makelabel{loops:QuasigroupFromFile}{4.5.1}
\makelabel{loops:LoopFromFile}{4.5.1}
\makelabel{loops:Creating quasigroups and loops by sections}{4.6}
\makelabel{loops:CayleyTableByPerms}{4.6.1}
\makelabel{loops:QuasigroupByLeftSection}{4.6.2}
\makelabel{loops:LoopByLeftSection}{4.6.2}
\makelabel{loops:QuasigroupByRightSection}{4.6.3}
\makelabel{loops:LoopByRightSection}{4.6.3}
\makelabel{loops:QuasigroupByRightSection}{4.6.4}
\makelabel{loops:LoopByRightSection}{4.6.4}
\makelabel{loops:Creating quasigroups and loops by extensions}{4.7}
\makelabel{loops:NuclearExtension}{4.7.1}
\makelabel{loops:LoopByExtension}{4.7.2}
\makelabel{loops:Random quasigroups and loops}{4.8}
\makelabel{loops:random!Latin square}{4.8}
\makelabel{loops:RandomLoop}{4.8.1}
\makelabel{loops:RandomLoop}{4.8.2}
\makelabel{loops:RandomQuasigroup}{4.8.3}
\makelabel{loops:RandomQuasigroup}{4.8.3}
\makelabel{loops:RandomNilpotentLoop}{4.8.4}
\makelabel{loops:Conversions}{4.9}
\makelabel{loops:IntoQuasigroup}{4.9.1}
\makelabel{loops:PrincipalLoopIsotope}{4.9.2}
\makelabel{loops:IntoLoop}{4.9.3}
\makelabel{loops:IntoGroup}{4.9.4}
\makelabel{loops:Products of loops}{4.10}
\makelabel{loops:DirectProduct}{4.10.1}
\makelabel{loops:Opposite quasigroups and loops}{4.11}
\makelabel{loops:Opposite}{4.11.1}
\makelabel{loops:Basic methods and attributes}{5}
\makelabel{loops:Basic attributes}{5.1}
\makelabel{loops:Elements}{5.1.1}
\makelabel{loops:CayleyTable}{5.1.2}
\makelabel{loops:One}{5.1.3}
\makelabel{loops:MultiplicativeNeutralElement}{5.1.4}
\makelabel{loops:Size}{5.1.5}
\makelabel{loops:Exponent}{5.1.6}
\makelabel{loops:Basic arithmetic operations}{5.2}
\makelabel{loops:LeftDivision}{5.2.1}
\makelabel{loops:RightDivision}{5.2.1}
\makelabel{loops:LeftDivision}{5.2.2}
\makelabel{loops:LeftDivision}{5.2.2}
\makelabel{loops:RightDivision}{5.2.2}
\makelabel{loops:RightDivision}{5.2.2}
\makelabel{loops:LeftDivisionCayleyTable}{5.2.3}
\makelabel{loops:RightDivisionCayleyTable}{5.2.3}
\makelabel{loops:Powers and inverses}{5.3}
\makelabel{loops:LeftInverse}{5.3.1}
\makelabel{loops:RightInverse}{5.3.1}
\makelabel{loops:Inverse}{5.3.1}
\makelabel{loops:Associators and commutators}{5.4}
\makelabel{loops:Associator}{5.4.1}
\makelabel{loops:Commutator}{5.4.1}
\makelabel{loops:Generators}{5.5}
\makelabel{loops:GeneratorsOfQuasigroup}{5.5.1}
\makelabel{loops:GeneratorsOfLoop}{5.5.1}
\makelabel{loops:GeneratorsSmallest}{5.5.2}
\makelabel{loops:Methods based on permutation groups}{6}
\makelabel{loops:Parent of a quasigroup}{6.1}
\makelabel{loops:Parent}{6.1.1}
\makelabel{loops:Position}{6.1.2}
\makelabel{loops:PosInParent}{6.1.3}
\makelabel{loops:Comparing quasigroups with common parent}{6.2}
\makelabel{loops:Subquasigroups and subloops}{6.3}
\makelabel{loops:Subquasigroup}{6.3.1}
\makelabel{loops:Subloop}{6.3.1}
\makelabel{loops:IsSubquasigroup}{6.3.2}
\makelabel{loops:IsSubloop}{6.3.2}
\makelabel{loops:AllSubloops}{6.3.3}
\makelabel{loops:RightCosets}{6.3.4}
\makelabel{loops:RightTransversal}{6.3.5}
\makelabel{loops:Translations and sections}{6.4}
\makelabel{loops:LeftTranslation}{6.4.1}
\makelabel{loops:RightTranslation}{6.4.1}
\makelabel{loops:LeftSection}{6.4.2}
\makelabel{loops:RightSection}{6.4.2}
\makelabel{loops:Multiplication groups}{6.5}
\makelabel{loops:LeftMultiplicationGroup}{6.5.1}
\makelabel{loops:RightMultiplicationGroup}{6.5.1}
\makelabel{loops:MultiplicationGroup}{6.5.1}
\makelabel{loops:RelativeLeftMultiplicationGroup}{6.5.2}
\makelabel{loops:RelativeRightMultiplicationGroup}{6.5.2}
\makelabel{loops:RelativeMultiplicationGroup}{6.5.2}
\makelabel{loops:Inner mapping groups}{6.6}
\makelabel{loops:LeftInnerMapping}{6.6.1}
\makelabel{loops:MiddleInnerMapping}{6.6.1}
\makelabel{loops:RightInnerMapping}{6.6.1}
\makelabel{loops:LeftInnerMappingGroup}{6.6.1}
\makelabel{loops:MiddleInnerMappingGroup}{6.6.1}
\makelabel{loops:RightInnerMappingGroup}{6.6.1}
\makelabel{loops:InnerMappingGroup}{6.6.1}
\makelabel{loops:Nuclei, commutant, center, and associator subloop}{6.7}
\makelabel{loops:LeftNucleus}{6.7.1}
\makelabel{loops:MiddleNucleus}{6.7.1}
\makelabel{loops:RightNucleus}{6.7.1}
\makelabel{loops:Nuc}{6.7.1}
\makelabel{loops:NucleusOfLoop}{6.7.2}
\makelabel{loops:NucleusOfQuasigroup}{6.7.2}
\makelabel{loops:Commutant}{6.7.3}
\makelabel{loops:Center}{6.7.4}
\makelabel{loops:AssociatorSubloop}{6.7.5}
\makelabel{loops:Normal subloops}{6.8}
\makelabel{loops:IsNormal}{6.8.1}
\makelabel{loops:NormalClosure}{6.8.2}
\makelabel{loops:IsSimple}{6.8.3}
\makelabel{loops:Factor loops}{6.9}
\makelabel{loops:FactorLoop}{6.9.1}
\makelabel{loops:NaturalHomomorphismByNormalSubloop}{6.9.2}
\makelabel{loops:Nilpotency and central series}{6.10}
\makelabel{loops:NilpotencyClassOfLoop}{6.10.1}
\makelabel{loops:IsNilpotent}{6.10.1}
\makelabel{loops:IsStronglyNilpotent}{6.10.2}
\makelabel{loops:UpperCentralSeries}{6.10.3}
\makelabel{loops:LowerCentralSeries}{6.10.4}
\makelabel{loops:Solvability}{6.11}
\makelabel{loops:IsSolvable}{6.11.1}
\makelabel{loops:DerivedSubloop}{6.11.1}
\makelabel{loops:DerivedLength}{6.11.1}
\makelabel{loops:FrattiniSubloop}{6.11.1}
\makelabel{loops:FrattinifactorSize}{6.11.1}
\makelabel{loops:Isomorphisms and automorphisms}{6.12}
\makelabel{loops:IsomorphismLoops}{6.12.1}
\makelabel{loops:LoopsUpToIsomorphism}{6.12.2}
\makelabel{loops:AutomorphismGroup}{6.12.3}
\makelabel{loops:IsomorphicCopyByPerm}{6.12.4}
\makelabel{loops:IsomorphicCopyByNormalSubloop}{6.12.5}
\makelabel{loops:How are isomorphisms computed}{6.13}
\makelabel{loops:Discriminator}{6.13.1}
\makelabel{loops:AreEqualDiscriminators}{6.13.2}
\makelabel{loops:Isotopisms}{6.14}
\makelabel{loops:IsotopismLoops}{6.14.1}
\makelabel{loops:LoopsUpToIsotopism}{6.14.2}
\makelabel{loops:Testing properties of quasigroups and loops}{7}
\makelabel{loops:Associativity, commutativity and generalizations}{7.1}
\makelabel{loops:IsAssociative}{7.1.1}
\makelabel{loops:IsCommutative}{7.1.1}
\makelabel{loops:IsPowerAssociative}{7.1.2}
\makelabel{loops:IsDiassociative}{7.1.2}
\makelabel{loops:Inverse properties}{7.2}
\makelabel{loops:HasLeftInverseProperty}{7.2.1}
\makelabel{loops:HasRightInverseProperty}{7.2.1}
\makelabel{loops:HasInverseProperty}{7.2.1}
\makelabel{loops:HasTwosidedInverses}{7.2.1}
\makelabel{loops:HasWeakInverseProperty}{7.2.2}
\makelabel{loops:HasAutomorphicInverseProperty}{7.2.3}
\makelabel{loops:HasAntiautomorphicInverseProperty}{7.2.3}
\makelabel{loops:Some properties of quasigroups}{7.3}
\makelabel{loops:IsSemisymmetric}{7.3.1}
\makelabel{loops:IsTotallySymmetric}{7.3.1}
\makelabel{loops:IsIdempotent}{7.3.2}
\makelabel{loops:IsSteinerQuasigroup}{7.3.2}
\makelabel{loops:IsUnipotent}{7.3.2}
\makelabel{loops:IsLeftDistributive}{7.3.3}
\makelabel{loops:IsRightDistributive}{7.3.3}
\makelabel{loops:IsDistributive}{7.3.3}
\makelabel{loops:IsEntropic}{7.3.3}
\makelabel{loops:IsMedial}{7.3.3}
\makelabel{loops:IsLDistributive}{7.3.4}
\makelabel{loops:IsRDistributive}{7.3.4}
\makelabel{loops:Loops of Bol-Moufang type}{7.4}
\makelabel{loops:IsExtraLoop}{7.4.1}
\makelabel{loops:IsMoufangLoop}{7.4.1}
\makelabel{loops:IsCLoop}{7.4.1}
\makelabel{loops:IsLeftBolLoop}{7.4.1}
\makelabel{loops:IsRightBolLoop}{7.4.1}
\makelabel{loops:IsLCLoop}{7.4.1}
\makelabel{loops:IsRCLoop}{7.4.1}
\makelabel{loops:IsLeftNuclearSquareLoop}{7.4.1}
\makelabel{loops:IsMiddleNuclearSquareLoop}{7.4.1}
\makelabel{loops:IsRightNuclearSquareLoop}{7.4.1}
\makelabel{loops:IsNuclearSquareLoop}{7.4.1}
\makelabel{loops:IsFlexible}{7.4.1}
\makelabel{loops:IsLeftAlternative}{7.4.1}
\makelabel{loops:IsRightAlternative}{7.4.1}
\makelabel{loops:IsAlternative}{7.4.1}
\makelabel{loops:Power alternative loops}{7.5}
\makelabel{loops:IsLeftPowerAlternative}{7.5.1}
\makelabel{loops:IsRightPowerAlternative}{7.5.1}
\makelabel{loops:IsPowerAlternative}{7.5.1}
\makelabel{loops:Conjugacy closed loops and related properties}{7.6}
\makelabel{loops:IsLCCLoop}{7.6.1}
\makelabel{loops:IsRCCLoop}{7.6.1}
\makelabel{loops:IsCCLoop}{7.6.1}
\makelabel{loops:IsOsbornLoop}{7.6.2}
\makelabel{loops:Additional varieties of loops}{7.7}
\makelabel{loops:IsCodeLoop}{7.7.1}
\makelabel{loops:IsSteinerLoop}{7.7.2}
\makelabel{loops:IsLeftBruckLoop}{7.7.3}
\makelabel{loops:IsLeftKLoop}{7.7.3}
\makelabel{loops:IsRightBruckLoop}{7.7.3}
\makelabel{loops:IsRightKLoop}{7.7.3}
\makelabel{loops:IsLeftAutomorphicLoop}{7.7.4}
\makelabel{loops:IsMiddleAutomorphicLoop}{7.7.4}
\makelabel{loops:IsRightAutomorphicLoop}{7.7.4}
\makelabel{loops:IsAutomorphicLoop}{7.7.4}
\makelabel{loops:IsLeftALoop}{7.7.5}
\makelabel{loops:IsMiddleALoop}{7.7.5}
\makelabel{loops:IsRightALoop}{7.7.5}
\makelabel{loops:IsALoop}{7.7.5}
\makelabel{loops:Specific methods}{8}
\makelabel{loops:Core methods for Bol loops}{8.1}
\makelabel{loops:AssociatedLeftBruckLoop}{8.1.1}
\makelabel{loops:Moufang modifications}{8.2}
\makelabel{loops:LoopByCyclicModification}{8.2.1}
\makelabel{loops:LoopByDihedralModification}{8.2.2}
\makelabel{loops:LoopMG2}{8.2.3}
\makelabel{loops:Triality for Moufang loops}{8.3}
\makelabel{loops:TrialityPermGroup}{8.3.1}
\makelabel{loops:TrialityPcGroup}{8.3.2}
\makelabel{loops:Realizing groups as multiplication groups of loops}{8.4}
\makelabel{loops:AllLoopTablesInGroup}{8.4.1}
\makelabel{loops:AllProperLoopTablesInGroup}{8.4.1}
\makelabel{loops:OneLoopTableInGroup}{8.4.1}
\makelabel{loops:OneProperLoopTableInGroup}{8.4.1}
\makelabel{loops:AllLoopsWithMltGroup}{8.4.1}
\makelabel{loops:OneLoopWithMltGroup}{8.4.1}
\makelabel{loops:Libraries of small loops}{9}
\makelabel{loops:lib}{9}
\makelabel{loops:A typical library}{9.1}
\makelabel{loops:MyLibraryLoop}{9.1.1}
\makelabel{loops:LibraryLoop}{9.1.2}
\makelabel{loops:DisplayLibraryInfo}{9.1.3}
\makelabel{loops:Left Bol loops}{9.2}
\makelabel{loops:LeftBolLoop}{9.2.1}
\makelabel{loops:Moufang loops}{9.3}
\makelabel{loops:MoufangLoop}{9.3.1}
\makelabel{loops:Code loops}{9.4}
\makelabel{loops:CodeLoop}{9.4.1}
\makelabel{loops:Steiner loops}{9.5}
\makelabel{loops:SteinerLoop}{9.5.1}
\makelabel{loops:CC-loops}{9.6}
\makelabel{loops:CCLoop}{9.6.1}
\makelabel{loops:Small loops}{9.7}
\makelabel{loops:SmallLoop}{9.7.1}
\makelabel{loops:Paige loops}{9.8}
\makelabel{loops:PaigeLoop}{9.8.1}
\makelabel{loops:Nilpotent loops}{9.9}
\makelabel{loops:NilpotentLoop}{9.9.1}
\makelabel{loops:Automorphic loops}{9.10}
\makelabel{loops:AutomorphicLoop}{9.10.1}
\makelabel{loops:Interesting loops}{9.11}
\makelabel{loops:InterestingLoop}{9.11.1}
\makelabel{loops:Libraries of loops up to isotopism}{9.12}
\makelabel{loops:ItpSmallLoop}{9.12.1}
\makelabel{loops:Files}{A}
\makelabel{loops:Filters built into the package}{B}
\makelabel{loops:Bibliography}{}
\setcitlab {Ar}{1}
\setcitlab {Br}{2}
\setcitlab {ChPfSm}{3}
\setcitlab {CoRo}{4}
\setcitlab {CsDr}{5}
\setcitlab {DaVo}{6}
\setcitlab {DrVo}{7}
\setcitlab {Fe}{8}
\setcitlab {Go}{9}
\setcitlab {JaMa}{10}
\setcitlab {KiKuPh}{11}
\setcitlab {Ku}{12}
\setcitlab {Li}{13}
\setcitlab {Mo}{14}
\setcitlab {Na}{15}
\setcitlab {NaVo2003}{16}
\setcitlab {NaVo2007}{17}
\setcitlab {Pf}{18}
\setcitlab {PhVo}{19}
\setcitlab {SlZe2011}{20}
\setcitlab {Vo}{21}
\setcitlab {Wi}{22}
\makelabel{loops:Index}{}
