\indexentry{list of files|href{#list of files11}}{1.1}
\indexentry{groupoid|href{#groupoid14}}{1.4}
\indexentry{magma|href{#magma14}}{1.4}
\indexentry{semigroup|href{#semigroup14}}{1.4}
\indexentry{neutral element|href{#neutral element14}}{1.4}
\indexentry{identity element|href{#identity element14}}{1.4}
\indexentry{monoid|href{#monoid14}}{1.4}
\indexentry{two-sided inverse|href{#two-sided inverse14}}{1.4}
\indexentry{group|href{#group14}}{1.4}
\indexentry{quasigroup|href{#quasigroup14}}{1.4}
\indexentry{Latin square|href{#Latin square14}}{1.4}
\indexentry{loop|href{#loop14}}{1.4}
\indexentry{left translation|href{#left translation14}}{1.4}
\indexentry{right translation|href{#right translation14}}{1.4}
\indexentry{left section|href{#left section14}}{1.4}
\indexentry{right section|href{#right section14}}{1.4}
\indexentry{left
multiplication group|href{#left
multiplication group14}}{1.4}
\indexentry{right multiplication group|href{#right multiplication group14}}{1.4}
\indexentry{multiplication group|href{#multiplication group14}}{1.4}
\indexentry{homomorphism|href{#homomorphism14}}{1.4}
\indexentry{isomorphism|href{#isomorphism14}}{1.4}
\indexentry{homotopism|href{#homotopism14}}{1.4}
\indexentry{isotopism|href{#isotopism14}}{1.4}
\indexentry{principal
isotopism|href{#principal
isotopism14}}{1.4}
\indexentry{principal loop isotope|href{#principal loop isotope14}}{1.4}
\indexentry{AsLoop|href{#AsLoop15}}{1.5}
\indexentry{AsQuasigroup|href{#AsQuasigroup15}}{1.5}
\indexentry{AsLoop|href{#AsLoop15}}{1.5}
\indexentry{SetQuasigroupElmName|href{#SetQuasigroupElmName21}}{2.1}
\indexentry{SetLoopElmName|href{#SetLoopElmName21}}{2.1}
\indexentry{Cayley table|href{#Cayley table22}}{2.2}
\indexentry{IsQuasigroupTable|href{#IsQuasigroupTable22}}{2.2}
\indexentry{IsQuasigroupCayleyTable|href{#IsQuasigroupCayleyTable22}}{2.2}
\indexentry{normalized Latin square|href{#normalized Latin square22}}{2.2}
\indexentry{IsLoopTable|href{#IsLoopTable22}}{2.2}
\indexentry{IsLoopCayleyTable|href{#IsLoopCayleyTable22}}{2.2}
\indexentry{NormalizedQuasigroupTable|href{#NormalizedQuasigroupTable22}}{2.2}
\indexentry{QuasigroupByCayleyTable|href{#QuasigroupByCayleyTable22}}{2.2}
\indexentry{QuasigroupByCayleyTable|href{#QuasigroupByCayleyTable22}}{2.2}
\indexentry{LoopByCayleyTable|href{#LoopByCayleyTable22}}{2.2}
\indexentry{QuasigroupFromFile|href{#QuasigroupFromFile22}}{2.2}
\indexentry{LoopFromFile|href{#LoopFromFile22}}{2.2}
\indexentry{AsQuasigroup|href{#AsQuasigroup22}}{2.2}
\indexentry{AsLoop|href{#AsLoop22}}{2.2}
\indexentry{PrincipalLoopIsotope|href{#PrincipalLoopIsotope22}}{2.2}
\indexentry{AsGroup|href{#AsGroup22}}{2.2}
\indexentry{DirectProduct|href{#DirectProduct22}}{2.2}
\indexentry{opposite quasigroup|href{#opposite quasigroup22}}{2.2}
\indexentry{Opposite|href{#Opposite22}}{2.2}
\indexentry{IsQuasigroupElement|href{#IsQuasigroupElement23}}{2.3}
\indexentry{IsLoopElement|href{#IsLoopElement23}}{2.3}
\indexentry{IsQuasigroup|href{#IsQuasigroup23}}{2.3}
\indexentry{IsLoop|href{#IsLoop23}}{2.3}
\indexentry{Elements|href{#Elements24}}{2.4}
\indexentry{CayleyTable|href{#CayleyTable24}}{2.4}
\indexentry{One|href{#One24}}{2.4}
\indexentry{MultiplicativeNeutralElement|href{#MultiplicativeNeutralElement24}}{2.4}
\indexentry{Size|href{#Size24}}{2.4}
\indexentry{exponent|href{#exponent24}}{2.4}
\indexentry{Exponent|href{#Exponent24}}{2.4}
\indexentry{left division|href{#left division25}}{2.5}
\indexentry{right division|href{#right division25}}{2.5}
\indexentry{LeftDivision|href{#LeftDivision25}}{2.5}
\indexentry{RightDivision|href{#RightDivision25}}{2.5}
\indexentry{monoassociative|href{#monoassociative25}}{2.5}
\indexentry{power associative|href{#power associative25}}{2.5}
\indexentry{left inverse|href{#left inverse25}}{2.5}
\indexentry{right inverse|href{#right inverse25}}{2.5}
\indexentry{inverse|href{#inverse25}}{2.5}
\indexentry{LeftInverse|href{#LeftInverse25}}{2.5}
\indexentry{RightInverse|href{#RightInverse25}}{2.5}
\indexentry{Inverse|href{#Inverse25}}{2.5}
\indexentry{associator|href{#associator25}}{2.5}
\indexentry{commutator|href{#commutator25}}{2.5}
\indexentry{Associator|href{#Associator25}}{2.5}
\indexentry{Commutator|href{#Commutator25}}{2.5}
\indexentry{GeneratorsOfQuasigroup|href{#GeneratorsOfQuasigroup26}}{2.6}
\indexentry{GeneratorsOfLoop|href{#GeneratorsOfLoop26}}{2.6}
\indexentry{SmallGeneratingSet|href{#SmallGeneratingSet26}}{2.6}
\indexentry{LeftSection|href{#LeftSection27}}{2.7}
\indexentry{RightSection|href{#RightSection27}}{2.7}
\indexentry{LeftTranslation|href{#LeftTranslation27}}{2.7}
\indexentry{RightTranslation|href{#RightTranslation27}}{2.7}
\indexentry{LeftMultiplicationGroup|href{#LeftMultiplicationGroup27}}{2.7}
\indexentry{RightMultiplicationGroup|href{#RightMultiplicationGroup27}}{2.7}
\indexentry{MultiplicationGroup|href{#MultiplicationGroup27}}{2.7}
\indexentry{RelativeLeftMultiplicationGroup|href{#RelativeLeftMultiplicationGroup27}}{2.7}
\indexentry{RelativeRightMultiplicationGroup|href{#RelativeRightMultiplicationGroup27}}{2.7}
\indexentry{RelativeMultiplicationGroup|href{#RelativeMultiplicationGroup27}}{2.7}
\indexentry{inner mapping group|href{#inner mapping group27}}{2.7}
\indexentry{InnerMappingGroup|href{#InnerMappingGroup27}}{2.7}
\indexentry{Parent|href{#Parent28}}{2.8}
\indexentry{PosInParent|href{#PosInParent28}}{2.8}
\indexentry{Subquasigroup|href{#Subquasigroup28}}{2.8}
\indexentry{Subloop|href{#Subloop28}}{2.8}
\indexentry{IsSubquasigroup|href{#IsSubquasigroup28}}{2.8}
\indexentry{IsSubloop|href{#IsSubloop28}}{2.8}
\indexentry{left nucleus|href{#left nucleus29}}{2.9}
\indexentry{middle nucleus|href{#middle nucleus29}}{2.9}
\indexentry{right nucleus|href{#right nucleus29}}{2.9}
\indexentry{nucleus|href{#nucleus29}}{2.9}
\indexentry{LeftNucleus|href{#LeftNucleus29}}{2.9}
\indexentry{MiddleNucleus|href{#MiddleNucleus29}}{2.9}
\indexentry{RightNucleus|href{#RightNucleus29}}{2.9}
\indexentry{Nuc|href{#Nuc29}}{2.9}
\indexentry{NucleusOfLoop|href{#NucleusOfLoop29}}{2.9}
\indexentry{NucleusOfQuasigroup|href{#NucleusOfQuasigroup29}}{2.9}
\indexentry{commutant|href{#commutant29}}{2.9}
\indexentry{Moufang center|href{#Moufang center29}}{2.9}
\indexentry{Commutant|href{#Commutant29}}{2.9}
\indexentry{Center|href{#Center29}}{2.9}
\indexentry{associator subloop|href{#associator subloop29}}{2.9}
\indexentry{AssociatorSubloop|href{#AssociatorSubloop29}}{2.9}
\indexentry{IsAssociative|href{#IsAssociative210}}{2.10}
\indexentry{IsCommutative|href{#IsCommutative210}}{2.10}
\indexentry{power associativity|href{#power associativity210}}{2.10}
\indexentry{diassoicativy|href{#diassoicativy210}}{2.10}
\indexentry{IsPowerAssociative|href{#IsPowerAssociative210}}{2.10}
\indexentry{IsDiassociative|href{#IsDiassociative210}}{2.10}
\indexentry{left inverse property|href{#left inverse property210}}{2.10}
\indexentry{right inverse property|href{#right inverse property210}}{2.10}
\indexentry{inverse property|href{#inverse property210}}{2.10}
\indexentry{two-sided inverses|href{#two-sided inverses210}}{2.10}
\indexentry{HasLeftInverseProperty|href{#HasLeftInverseProperty210}}{2.10}
\indexentry{HasRightInverseProperty|href{#HasRightInverseProperty210}}{2.10}
\indexentry{HasInverseProperty|href{#HasInverseProperty210}}{2.10}
\indexentry{HasTwosidedInverses|href{#HasTwosidedInverses210}}{2.10}
\indexentry{automorphic
inverse property|href{#automorphic
inverse property210}}{2.10}
\indexentry{antiautomorphic inverse property|href{#antiautomorphic inverse property210}}{2.10}
\indexentry{HasAutomorphicInverseProperty|href{#HasAutomorphicInverseProperty210}}{2.10}
\indexentry{HasAntiautomorphicInverseProperty|href{#HasAntiautomorphicInverseProperty210}}{2.10}
\indexentry{semisymmetric
quasigroup|href{#semisymmetric
quasigroup210}}{2.10}
\indexentry{totally
symmetric quasigroup|href{#totally
symmetric quasigroup210}}{2.10}
\indexentry{IsSemisymmetric|href{#IsSemisymmetric210}}{2.10}
\indexentry{IsTotallySymmetric|href{#IsTotallySymmetric210}}{2.10}
\indexentry{idempotent|href{#idempotent210}}{2.10}
\indexentry{Steiner quasigroup|href{#Steiner quasigroup210}}{2.10}
\indexentry{unipotent quasigroup|href{#unipotent quasigroup210}}{2.10}
\indexentry{IsIdempotent|href{#IsIdempotent210}}{2.10}
\indexentry{IsSteinerQuasigroup|href{#IsSteinerQuasigroup210}}{2.10}
\indexentry{IsUnipotent|href{#IsUnipotent210}}{2.10}
\indexentry{left distributive
quasigroup|href{#left distributive
quasigroup210}}{2.10}
\indexentry{right distributive quasigroup|href{#right distributive quasigroup210}}{2.10}
\indexentry{distributive quasigroup|href{#distributive quasigroup210}}{2.10}
\indexentry{entropic quasigroup|href{#entropic quasigroup210}}{2.10}
\indexentry{medial
quasigroup|href{#medial
quasigroup210}}{2.10}
\indexentry{IsLeftDistributive|href{#IsLeftDistributive210}}{2.10}
\indexentry{IsRightDistributive|href{#IsRightDistributive210}}{2.10}
\indexentry{IsDistributive|href{#IsDistributive210}}{2.10}
\indexentry{IsEntropic|href{#IsEntropic210}}{2.10}
\indexentry{IsMedial|href{#IsMedial210}}{2.10}
\indexentry{IsLDistributive|href{#IsLDistributive210}}{2.10}
\indexentry{IsRDistributive|href{#IsRDistributive210}}{2.10}
\indexentry{loops of Bol-Moufang type|href{#loops of Bol-Moufang type210}}{2.10}
\indexentry{alternative loop|href{#alternative loop210}}{2.10}
\indexentry{nuclear square loop|href{#nuclear square loop210}}{2.10}
\indexentry{IsExtraLoop|href{#IsExtraLoop210}}{2.10}
\indexentry{IsMoufangLoop|href{#IsMoufangLoop210}}{2.10}
\indexentry{IsCLoop|href{#IsCLoop210}}{2.10}
\indexentry{IsLeftBolLoop|href{#IsLeftBolLoop210}}{2.10}
\indexentry{IsRightBolLoop|href{#IsRightBolLoop210}}{2.10}
\indexentry{IsLCLoop|href{#IsLCLoop210}}{2.10}
\indexentry{IsRCLoop|href{#IsRCLoop210}}{2.10}
\indexentry{IsLeftNuclearSquareLoop|href{#IsLeftNuclearSquareLoop210}}{2.10}
\indexentry{IsMiddleNuclearSquareLoop|href{#IsMiddleNuclearSquareLoop210}}{2.10}
\indexentry{IsRightNuclearSquareLoop|href{#IsRightNuclearSquareLoop210}}{2.10}
\indexentry{IsNuclearSquareLoop|href{#IsNuclearSquareLoop210}}{2.10}
\indexentry{IsFlexible|href{#IsFlexible210}}{2.10}
\indexentry{IsLeftAlternative|href{#IsLeftAlternative210}}{2.10}
\indexentry{IsRightAlternative|href{#IsRightAlternative210}}{2.10}
\indexentry{IsAlternative|href{#IsAlternative210}}{2.10}
\indexentry{left conjugacy closed loop|href{#left conjugacy closed loop210}}{2.10}
\indexentry{right conjugacy closed loop|href{#right conjugacy closed loop210}}{2.10}
\indexentry{conjugacy closed loop|href{#conjugacy closed loop210}}{2.10}
\indexentry{IsLCCLoop|href{#IsLCCLoop210}}{2.10}
\indexentry{IsRCCLoop|href{#IsRCCLoop210}}{2.10}
\indexentry{IsCCLoop|href{#IsCCLoop210}}{2.10}
\indexentry{left Bruck loop|href{#left Bruck loop210}}{2.10}
\indexentry{right Bruck loop|href{#right Bruck loop210}}{2.10}
\indexentry{K-loop|href{#K-loop210}}{2.10}
\indexentry{IsLeftBruckLoop|href{#IsLeftBruckLoop210}}{2.10}
\indexentry{IsLeftKLoop|href{#IsLeftKLoop210}}{2.10}
\indexentry{IsRightBruckLoop|href{#IsRightBruckLoop210}}{2.10}
\indexentry{IsRightKLoop|href{#IsRightKLoop210}}{2.10}
\indexentry{Steiner loop|href{#Steiner loop210}}{2.10}
\indexentry{IsSteinerLoop|href{#IsSteinerLoop210}}{2.10}
\indexentry{normal subloop|href{#normal subloop211}}{2.11}
\indexentry{IsNormal|href{#IsNormal211}}{2.11}
\indexentry{normal closure|href{#normal closure211}}{2.11}
\indexentry{NormalClosure|href{#NormalClosure211}}{2.11}
\indexentry{simple loop|href{#simple loop211}}{2.11}
\indexentry{IsSimple|href{#IsSimple211}}{2.11}
\indexentry{FactorLoop|href{#FactorLoop212}}{2.12}
\indexentry{NaturalHomomorphismByNormalSubloop|href{#NaturalHomomorphismByNormalSubloop212}}{2.12}
\indexentry{NilpotencyClassOfLoop|href{#NilpotencyClassOfLoop213}}{2.13}
\indexentry{IsNilpotent|href{#IsNilpotent213}}{2.13}
\indexentry{strongly nilpotent
loop|href{#strongly nilpotent
loop213}}{2.13}
\indexentry{IsStronglyNilpotent|href{#IsStronglyNilpotent213}}{2.13}
\indexentry{IsSolvable|href{#IsSolvable214}}{2.14}
\indexentry{DerivedSubloop|href{#DerivedSubloop214}}{2.14}
\indexentry{DerivedLength|href{#DerivedLength214}}{2.14}
\indexentry{FrattiniSubloop|href{#FrattiniSubloop214}}{2.14}
\indexentry{FrattinifactorSize|href{#FrattinifactorSize214}}{2.14}
\indexentry{IsomorphismLoops|href{#IsomorphismLoops31}}{3.1}
\indexentry{AutomorphismGroup|href{#AutomorphismGroup31}}{3.1}
\indexentry{Discriminator|href{#Discriminator31}}{3.1}
\indexentry{AreEqualDiscriminators|href{#AreEqualDiscriminators31}}{3.1}
\indexentry{EfficientGenerators|href{#EfficientGenerators31}}{3.1}
\indexentry{Moufang modifications|href{#Moufang modifications32}}{3.2}
\indexentry{cyclic modification|href{#cyclic modification32}}{3.2}
\indexentry{LoopByCyclicModification|href{#LoopByCyclicModification32}}{3.2}
\indexentry{dihedral modification|href{#dihedral modification32}}{3.2}
\indexentry{LoopByDihedralModification|href{#LoopByDihedralModification32}}{3.2}
\indexentry{LoopMG2|href{#LoopMG232}}{3.2}
\indexentry{group
with triality|href{#group
with triality33}}{3.3}
\indexentry{TrialityPermGroup|href{#TrialityPermGroup33}}{3.3}
\indexentry{TrialityPcGroup|href{#TrialityPcGroup33}}{3.3}
\indexentry{MyLibraryLoop|href{#MyLibraryLoop41}}{4.1}
\indexentry{LibraryLoop|href{#LibraryLoop41}}{4.1}
\indexentry{LeftBolLoop|href{#LeftBolLoop41}}{4.1}
\indexentry{LibraryLoop|href{#LibraryLoop41}}{4.1}
\indexentry{DisplayLibraryInfo|href{#DisplayLibraryInfo41}}{4.1}
\indexentry{LeftBolLoop|href{#LeftBolLoop42}}{4.2}
\indexentry{MoufangLoop|href{#MoufangLoop43}}{4.3}
\indexentry{octonions|href{#octonions43}}{4.3}
\indexentry{IsomorphismTypeOfMoufangLoop|href{#IsomorphismTypeOfMoufangLoop43}}{4.3}
\indexentry{SteinerLoop|href{#SteinerLoop44}}{4.4}
\indexentry{Paige loop|href{#Paige loop45}}{4.5}
\indexentry{PaigeLoop|href{#PaigeLoop45}}{4.5}
\indexentry{sedenions|href{#sedenions46}}{4.6}
\indexentry{InterestingLoop|href{#InterestingLoop46}}{4.6}
