\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:Mathematical background}{2}
\makelabel{loops:Quasigroups and loops}{2.1}
\makelabel{loops:Translations}{2.2}
\makelabel{loops:Homomorphisms and homotopisms}{2.3}
\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:AsLoop}{3.2.1}
\makelabel{loops:AsQuasigroup}{3.2.2}
\makelabel{loops:AsLoop}{3.2.2}
\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:Basic methods and attributes}{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:Conversions}{4.6}
\makelabel{loops:AsQuasigroup}{4.6.1}
\makelabel{loops:AsLoop}{4.6.2}
\makelabel{loops:PrincipalLoopIsotope}{4.6.3}
\makelabel{loops:AsGroup}{4.6.4}
\makelabel{loops:Products of loops}{4.7}
\makelabel{loops:DirectProduct}{4.7.1}
\makelabel{loops:Opposite quasigroups and loops}{4.8}
\makelabel{loops:Opposite}{4.8.1}
\makelabel{loops:Basic attributes}{4.9}
\makelabel{loops:Elements}{4.9.1}
\makelabel{loops:CayleyTable}{4.9.2}
\makelabel{loops:One}{4.9.3}
\makelabel{loops:MultiplicativeNeutralElement}{4.9.4}
\makelabel{loops:Size}{4.9.5}
\makelabel{loops:Exponent}{4.9.6}
\makelabel{loops:Basic arithmetic operations}{4.10}
\makelabel{loops:LeftDivision}{4.10.1}
\makelabel{loops:RightDivision}{4.10.1}
\makelabel{loops:LeftDivision}{4.10.2}
\makelabel{loops:LeftDivision}{4.10.2}
\makelabel{loops:RightDivision}{4.10.2}
\makelabel{loops:RightDivision}{4.10.2}
\makelabel{loops:Powers and inverses}{4.11}
\makelabel{loops:LeftInverse}{4.11.1}
\makelabel{loops:RightInverse}{4.11.1}
\makelabel{loops:Inverse}{4.11.1}
\makelabel{loops:Associators and commutators}{4.12}
\makelabel{loops:Associator}{4.12.1}
\makelabel{loops:Commutator}{4.12.1}
\makelabel{loops:Generators}{4.13}
\makelabel{loops:GeneratorsOfQuasigroup}{4.13.1}
\makelabel{loops:GeneratorsOfLoop}{4.13.1}
\makelabel{loops:GeneratorsSmallest}{4.13.2}
\makelabel{loops:Some methods based on permutation groups}{5}
\makelabel{loops:Parent of a quasigroup}{5.1}
\makelabel{loops:Parent}{5.1.1}
\makelabel{loops:Position}{5.1.2}
\makelabel{loops:PosInParent}{5.1.3}
\makelabel{loops:Comparing quasigroups with common parent}{5.2}
\makelabel{loops:Subquasigroups and subloops}{5.3}
\makelabel{loops:Subquasigroup}{5.3.1}
\makelabel{loops:Subloop}{5.3.1}
\makelabel{loops:IsSubquasigroup}{5.3.2}
\makelabel{loops:IsSubloop}{5.3.2}
\makelabel{loops:Translations and sections}{5.4}
\makelabel{loops:LeftTranslation}{5.4.1}
\makelabel{loops:RightTranslation}{5.4.1}
\makelabel{loops:LeftSection}{5.4.2}
\makelabel{loops:RightSection}{5.4.2}
\makelabel{loops:Multiplication groups}{5.5}
\makelabel{loops:LeftMultiplicationGroup}{5.5.1}
\makelabel{loops:RightMultiplicationGroup}{5.5.1}
\makelabel{loops:MultiplicationGroup}{5.5.1}
\makelabel{loops:RelativeLeftMultiplicationGroup}{5.5.2}
\makelabel{loops:RelativeRightMultiplicationGroup}{5.5.2}
\makelabel{loops:RelativeMultiplicationGroup}{5.5.2}
\makelabel{loops:Inner mapping groups}{5.6}
\makelabel{loops:InnerMappingGroup}{5.6.1}
\makelabel{loops:LeftInnerMappingGroup}{5.6.1}
\makelabel{loops:RightInnerMappingGroup}{5.6.1}
\makelabel{loops:Nuclei, commutant, center, and associator subloop}{5.7}
\makelabel{loops:LeftNucleus}{5.7.1}
\makelabel{loops:MiddleNucleus}{5.7.1}
\makelabel{loops:RightNucleus}{5.7.1}
\makelabel{loops:Nuc}{5.7.1}
\makelabel{loops:NucleusOfLoop}{5.7.2}
\makelabel{loops:NucleusOfQuasigroup}{5.7.3}
\makelabel{loops:Commutant}{5.7.4}
\makelabel{loops:Center}{5.7.5}
\makelabel{loops:AssociatorSubloop}{5.7.6}
\makelabel{loops:Normal subloops}{5.8}
\makelabel{loops:IsNormal}{5.8.1}
\makelabel{loops:NormalClosure}{5.8.2}
\makelabel{loops:IsSimple}{5.8.3}
\makelabel{loops:Factor loops}{5.9}
\makelabel{loops:FactorLoop}{5.9.1}
\makelabel{loops:NaturalHomomorphismByNormalSubloop}{5.9.2}
\makelabel{loops:Nilpotency and central series}{5.10}
\makelabel{loops:NilpotencyClassOfLoop}{5.10.1}
\makelabel{loops:IsNilpotent}{5.10.1}
\makelabel{loops:IsStronglyNilpotent}{5.10.2}
\makelabel{loops:UpperCentralSeries}{5.10.3}
\makelabel{loops:LowerCentralSeries}{5.10.4}
\makelabel{loops:Solvability}{5.11}
\makelabel{loops:IsSolvable}{5.11.1}
\makelabel{loops:DerivedSubloop}{5.11.1}
\makelabel{loops:DerivedLength}{5.11.1}
\makelabel{loops:FrattiniSubloop}{5.11.1}
\makelabel{loops:FrattinifactorSize}{5.11.1}
\makelabel{loops:Isomorphisms and automorphisms}{5.12}
\makelabel{loops:IsomorphismLoops}{5.12.1}
\makelabel{loops:AutomorphismGroup}{5.12.2}
\makelabel{loops:How are isomorphisms computed}{5.13}
\makelabel{loops:Discriminator}{5.13.1}
\makelabel{loops:AreEqualDiscriminators}{5.13.2}
\makelabel{loops:Testing properties of quasigroups and loops}{6}
\makelabel{loops:Associativity, commutativity and generalizations}{6.1}
\makelabel{loops:IsAssociative}{6.1.1}
\makelabel{loops:IsCommutative}{6.1.1}
\makelabel{loops:IsPowerAssociative}{6.1.2}
\makelabel{loops:IsDiassociative}{6.1.2}
\makelabel{loops:Inverse properties}{6.2}
\makelabel{loops:HasLeftInverseProperty}{6.2.1}
\makelabel{loops:HasRightInverseProperty}{6.2.1}
\makelabel{loops:HasInverseProperty}{6.2.1}
\makelabel{loops:HasTwosidedInverses}{6.2.1}
\makelabel{loops:HasWeakInverseProperty}{6.2.2}
\makelabel{loops:HasAutomorphicInverseProperty}{6.2.3}
\makelabel{loops:HasAntiautomorphicInverseProperty}{6.2.3}
\makelabel{loops:Some properties of quasigroups}{6.3}
\makelabel{loops:IsSemisymmetric}{6.3.1}
\makelabel{loops:IsTotallySymmetric}{6.3.1}
\makelabel{loops:IsIdempotent}{6.3.2}
\makelabel{loops:IsSteinerQuasigroup}{6.3.2}
\makelabel{loops:IsUnipotent}{6.3.2}
\makelabel{loops:IsLeftDistributive}{6.3.3}
\makelabel{loops:IsRightDistributive}{6.3.3}
\makelabel{loops:IsDistributive}{6.3.3}
\makelabel{loops:IsEntropic}{6.3.3}
\makelabel{loops:IsMedial}{6.3.3}
\makelabel{loops:IsLDistributive}{6.3.4}
\makelabel{loops:IsRDistributive}{6.3.4}
\makelabel{loops:Loops of Bol-Moufang type and related properties}{6.4}
\makelabel{loops:IsExtraLoop}{6.4.1}
\makelabel{loops:IsMoufangLoop}{6.4.1}
\makelabel{loops:IsCLoop}{6.4.1}
\makelabel{loops:IsLeftBolLoop}{6.4.1}
\makelabel{loops:IsRightBolLoop}{6.4.1}
\makelabel{loops:IsLCLoop}{6.4.1}
\makelabel{loops:IsRCLoop}{6.4.1}
\makelabel{loops:IsLeftNuclearSquareLoop}{6.4.1}
\makelabel{loops:IsMiddleNuclearSquareLoop}{6.4.1}
\makelabel{loops:IsRightNuclearSquareLoop}{6.4.1}
\makelabel{loops:IsNuclearSquareLoop}{6.4.1}
\makelabel{loops:IsFlexible}{6.4.1}
\makelabel{loops:IsLeftAlternative}{6.4.1}
\makelabel{loops:IsRightAlternative}{6.4.1}
\makelabel{loops:IsAlternative}{6.4.1}
\makelabel{loops:Conjugacy closed loops and related properties}{6.5}
\makelabel{loops:IsLCCLoop}{6.5.1}
\makelabel{loops:IsRCCLoop}{6.5.1}
\makelabel{loops:IsCCLoop}{6.5.1}
\makelabel{loops:IsOsbornLoop}{6.5.2}
\makelabel{loops:Additional varieties of loops}{6.6}
\makelabel{loops:IsLeftBruckLoop}{6.6.1}
\makelabel{loops:IsLeftKLoop}{6.6.1}
\makelabel{loops:IsRightBruckLoop}{6.6.1}
\makelabel{loops:IsRightKLoop}{6.6.1}
\makelabel{loops:IsSteinerLoop}{6.6.2}
\makelabel{loops:Specific methods}{7}
\makelabel{loops:Moufang modifications}{7.1}
\makelabel{loops:LoopByCyclicModification}{7.1.1}
\makelabel{loops:LoopByDihedralModification}{7.1.2}
\makelabel{loops:LoopMG2}{7.1.3}
\makelabel{loops:Triality for Moufang loops}{7.2}
\makelabel{loops:TrialityPermGroup}{7.2.1}
\makelabel{loops:TrialityPcGroup}{7.2.2}
\makelabel{loops:Libraries of small loops}{8}
\makelabel{loops:lib}{8}
\makelabel{loops:A typical library}{8.1}
\makelabel{loops:MyLibraryLoop}{8.1.1}
\makelabel{loops:LibraryLoop}{8.1.2}
\makelabel{loops:DisplayLibraryInfo}{8.1.3}
\makelabel{loops:Left Bol loops}{8.2}
\makelabel{loops:LeftBolLoop}{8.2.1}
\makelabel{loops:Small Moufang loops}{8.3}
\makelabel{loops:MoufangLoop}{8.3.1}
\makelabel{loops:IsomorphismTypeOfMoufangLoop}{8.3.2}
\makelabel{loops:Steiner loops}{8.4}
\makelabel{loops:SteinerLoop}{8.4.1}
\makelabel{loops:CC-loops}{8.5}
\makelabel{loops:CCLoop}{8.5.1}
\makelabel{loops:Paige loops}{8.6}
\makelabel{loops:PaigeLoop}{8.6.1}
\makelabel{loops:Interesting loops}{8.7}
\makelabel{loops:InterestingLoop}{8.7.1}
\makelabel{loops:Files}{A}
\makelabel{loops:Filters built into the package}{B}
\makelabel{loops:Bibliography}{}
\setcitlab {Ar}{1}
\setcitlab {Br}{2}
\setcitlab {Ch}{3}
\setcitlab {CR}{4}
\setcitlab {CD}{5}
\setcitlab {DV}{6}
\setcitlab {Fe}{7}
\setcitlab {Goodaire}{8}
\setcitlab {Kunen}{9}
\setcitlab {Li}{10}
\setcitlab {NV}{11}
\setcitlab {Pf}{12}
\setcitlab {PV}{13}
\setcitlab {VoEJC}{14}
\setcitlab {Wilson}{15}
\makelabel{loops:Index}{}
