\makelabel{sonata:Copyright notice}{{\setbox 0=\hbox {1}\vrule width 0pt height\ht 0}}
\makelabel{sonata:The authors}{{\setbox 0=\hbox {1}\vrule width 0pt height\ht 0}}
\makelabel{sonata:Preface}{{\setbox 0=\hbox {1}\vrule width 0pt height\ht 0}}
\makelabel{sonata:Supportive functions for groups}{1}
\makelabel{sonata:Predefined groups}{1.1}
\makelabel{sonata:TWGroup}{1.1.1}
\makelabel{sonata:IdTWGroup}{1.1.2}
\makelabel{sonata:Operation tables for groups}{1.2}
\makelabel{sonata:PrintTable}{1.2.1}
\makelabel{sonata:Group endomorphisms}{1.3}
\makelabel{sonata:Endomorphisms}{1.3.1}
\makelabel{sonata:Group automorphisms}{1.4}
\makelabel{sonata:Automorphisms}{1.4.1}
\makelabel{sonata:Inner automorphisms of a group}{1.5}
\makelabel{sonata:InnerAutomorphisms}{1.5.1}
\makelabel{sonata:Isomorphic groups}{1.6}
\makelabel{sonata:IsIsomorphicGroup}{1.6.1}
\makelabel{sonata:Subgroups of a group}{1.7}
\makelabel{sonata:Subgroups}{1.7.1}
\makelabel{sonata:Normal subgroups generated by a single element}{1.8}
\makelabel{sonata:OneGeneratedNormalSubgroups}{1.8.1}
\makelabel{sonata:Invariant subgroups}{1.9}
\makelabel{sonata:IsInvariantUnderMaps}{1.9.1}
\makelabel{sonata:IsCharacteristicSubgroup}{1.9.2}
\makelabel{sonata:IsCharacteristicInParent}{1.9.3}
\makelabel{sonata:IsFullinvariant}{1.9.4}
\makelabel{sonata:IsFullinvariantInParent}{1.9.5}
\makelabel{sonata:Coset representatives}{1.10}
\makelabel{sonata:RepresentativesModNormalSubgroup}{1.10.1}
\makelabel{sonata:NontrivialRepresentativesModNormalSubgroup}{1.10.2}
\makelabel{sonata:Nilpotency class}{1.11}
\makelabel{sonata:NilpotencyClass}{1.11.1}
\makelabel{sonata:Scott length}{1.12}
\makelabel{sonata:ScottLength}{1.12.1}
\makelabel{sonata:Other useful functions for groups}{1.13}
\makelabel{sonata:AsPermGroup}{1.13.1}
\makelabel{sonata:Nearrings}{2}
\makelabel{sonata:Defining a nearring multiplication}{2.1}
\makelabel{sonata:IsNearRingMultiplication}{2.1.1}
\makelabel{sonata:NearRingMultiplicationByOperationTable}{2.1.2}
\makelabel{sonata:Construction of nearrings}{2.2}
\makelabel{sonata:ExplicitMultiplicationNearRing}{2.2.1}
\makelabel{sonata:ExplicitMultiplicationNearRingNC}{2.2.2}
\makelabel{sonata:IsNearRing}{2.2.3}
\makelabel{sonata:IsExplicitMultiplicationNearRing}{2.2.4}
\makelabel{sonata:Direct products of nearrings}{2.3}
\makelabel{sonata:DirectProductNearRing}{2.3.1}
\makelabel{sonata:Operation tables for nearrings}{2.4}
\makelabel{sonata:PrintTable!near rings}{2.4.1}
\makelabel{sonata:Modified symbols for the operation tables}{2.5}
\makelabel{sonata:SetSymbols}{2.5.1}
\makelabel{sonata:SetSymbolsSupervised}{2.5.1}
\makelabel{sonata:Symbols}{2.5.2}
\makelabel{sonata:Accessing nearring elements}{2.6}
\makelabel{sonata:AsNearRingElement}{2.6.1}
\makelabel{sonata:AsGroupReductElement}{2.6.2}
\makelabel{sonata:Nearring elements}{2.7}
\makelabel{sonata:AsList!near rings}{2.7.1}
\makelabel{sonata:AsSortedList!near rings}{2.7.2}
\makelabel{sonata:Enumerator!near rings}{2.7.3}
\makelabel{sonata:Random nearring elements}{2.8}
\makelabel{sonata:Random!near ring element}{2.8.1}
\makelabel{sonata:Nearring generators}{2.9}
\makelabel{sonata:GeneratorsOfNearRing}{2.9.1}
\makelabel{sonata:Size of a nearring}{2.10}
\makelabel{sonata:Size!near rings}{2.10.1}
\makelabel{sonata:The additive group of a nearring}{2.11}
\makelabel{sonata:GroupReduct}{2.11.1}
\makelabel{sonata:Nearring endomorphisms}{2.12}
\makelabel{sonata:Endomorphisms!near rings}{2.12.1}
\makelabel{sonata:Nearring automorphisms}{2.13}
\makelabel{sonata:Automorphisms!near rings}{2.13.1}
\makelabel{sonata:Isomorphic nearrings}{2.14}
\makelabel{sonata:IsIsomorphicNearRing}{2.14.1}
\makelabel{sonata:Subnearrings}{2.15}
\makelabel{sonata:SubNearRings}{2.15.1}
\makelabel{sonata:Invariant subnearrings}{2.16}
\makelabel{sonata:InvariantSubNearRings}{2.16.1}
\makelabel{sonata:Constructing subnearrings}{2.17}
\makelabel{sonata:SubNearRingBySubgroupNC}{2.17.1}
\makelabel{sonata:Intersection of nearrings}{2.18}
\makelabel{sonata:Intersection!for nearrings}{2.18.1}
\makelabel{sonata:Identity of a nearring}{2.19}
\makelabel{sonata:Identity}{2.19.1}
\makelabel{sonata:One}{2.19.2}
\makelabel{sonata:IsNearRingWithOne}{2.19.3}
\makelabel{sonata:Units of a nearring}{2.20}
\makelabel{sonata:IsNearRingUnit}{2.20.1}
\makelabel{sonata:NearRingUnits}{2.20.2}
\makelabel{sonata:Distributivity in a nearring}{2.21}
\makelabel{sonata:Distributors}{2.21.1}
\makelabel{sonata:DistributiveElements}{2.21.2}
\makelabel{sonata:IsDistributiveNearRing}{2.21.3}
\makelabel{sonata:Elements of a nearring with special properties}{2.22}
\makelabel{sonata:ZeroSymmetricElements}{2.22.1}
\makelabel{sonata:IdempotentElements}{2.22.2}
\makelabel{sonata:NilpotentElements}{2.22.3}
\makelabel{sonata:QuasiregularElements}{2.22.4}
\makelabel{sonata:RegularElements}{2.22.5}
\makelabel{sonata:Special properties of a nearring}{2.23}
\makelabel{sonata:IsAbelianNearRing}{2.23.1}
\makelabel{sonata:IsAbstractAffineNearRing}{2.23.2}
\makelabel{sonata:IsBooleanNearRing}{2.23.3}
\makelabel{sonata:IsNilNearRing}{2.23.4}
\makelabel{sonata:IsNilpotentNearRing}{2.23.5}
\makelabel{sonata:IsNilpotentFreeNearRing}{2.23.6}
\makelabel{sonata:IsCommutative}{2.23.7}
\makelabel{sonata:IsDgNearRing}{2.23.8}
\makelabel{sonata:IsIntegralNearRing}{2.23.9}
\makelabel{sonata:IsPrimeNearRing}{2.23.10}
\makelabel{sonata:IsQuasiregularNearRing}{2.23.11}
\makelabel{sonata:IsRegularNearRing}{2.23.12}
\makelabel{sonata:IsNearField}{2.23.13}
\makelabel{sonata:IsPlanarNearRing}{2.23.14}
\makelabel{sonata:IsWdNearRing}{2.23.15}
\makelabel{sonata:The nearring library}{3}
\makelabel{sonata:Extracting nearrings from the library}{3.1}
\makelabel{sonata:LibraryNearRing}{3.1.1}
\makelabel{sonata:NumberLibraryNearRings}{3.1.2}
\makelabel{sonata:AllLibraryNearRings}{3.1.3}
\makelabel{sonata:LibraryNearRingWithOne}{3.1.4}
\makelabel{sonata:NumberLibraryNearRingsWithOne}{3.1.5}
\makelabel{sonata:AllLibraryNearRingsWithOne}{3.1.6}
\makelabel{sonata:Identifying nearrings}{3.2}
\makelabel{sonata:IdLibraryNearRing}{3.2.1}
\makelabel{sonata:IdLibraryNearRingWithOne}{3.2.2}
\makelabel{sonata:IsLibraryNearRing}{3.3}
\makelabel{sonata:IsLibraryNearRing}{3.3.1}
\makelabel{sonata:Accessing the information about a nearring stored in the library}{3.4}
\makelabel{sonata:LibraryNearRingInfo}{3.4.1}
\makelabel{sonata:Arbitrary functions on groups: EndoMappings}{4}
\makelabel{sonata:Defining endo mappings}{4.1}
\makelabel{sonata:EndoMappingByPositionList }{4.1.1}
\makelabel{sonata:EndoMappingByFunction}{4.1.2}
\makelabel{sonata:AsEndoMapping}{4.1.3}
\makelabel{sonata:AsGroupGeneralMappingByImages}{4.1.4}
\makelabel{sonata:IsEndoMapping}{4.1.5}
\makelabel{sonata:IdentityEndoMapping}{4.1.6}
\makelabel{sonata:ConstantEndoMapping}{4.1.7}
\makelabel{sonata:Properties of endo mappings}{4.2}
\makelabel{sonata:IsIdentityEndoMapping}{4.2.1}
\makelabel{sonata:IsConstantEndoMapping}{4.2.2}
\makelabel{sonata:IsDistributiveEndoMapping}{4.2.3}
\makelabel{sonata:Operations for endo mappings}{4.3}
\makelabel{sonata:Nicer ways to print a mapping}{4.4}
\makelabel{sonata:GraphOfMapping}{4.4.1}
\makelabel{sonata:PrintAsTerm}{4.4.2}
\makelabel{sonata:Transformation nearrings}{5}
\makelabel{sonata:Constructing transformation nearrings}{5.1}
\makelabel{sonata:TransformationNearRingByGenerators}{5.1.1}
\makelabel{sonata:TransformationNearRingByAdditiveGenerators}{5.1.2}
\makelabel{sonata:Nearrings of transformations}{5.2}
\makelabel{sonata:MapNearRing}{5.2.1}
\makelabel{sonata:TransformationNearRing}{5.2.2}
\makelabel{sonata:IsFullTransformationNearRing}{5.2.3}
\makelabel{sonata:PolynomialNearRing}{5.2.4}
\makelabel{sonata:EndomorphismNearRing}{5.2.5}
\makelabel{sonata:AutomorphismNearRing}{5.2.6}
\makelabel{sonata:InnerAutomorphismNearRing}{5.2.7}
\makelabel{sonata:CompatibleFunctionNearRing}{5.2.8}
\makelabel{sonata:ZeroSymmetricCompatibleFunctionNearRing}{5.2.9}
\makelabel{sonata:IsCompatibleEndoMapping}{5.2.10}
\makelabel{sonata:Is1AffineComplete}{5.2.11}
\makelabel{sonata:CentralizerNearRing}{5.2.12}
\makelabel{sonata:RestrictedEndomorphismNearRing}{5.2.13}
\makelabel{sonata:LocalInterpolationNearRing}{5.2.14}
\makelabel{sonata:The group a transformation nearring acts on}{5.3}
\makelabel{sonata:Gamma}{5.3.1}
\makelabel{sonata:Transformation nearrings and other nearrings}{5.4}
\makelabel{sonata:AsTransformationNearRing}{5.4.1}
\makelabel{sonata:AsExplicitMultiplicationNearRing}{5.4.2}
\makelabel{sonata:Noetherian quotients for transformation nearrings}{5.5}
\makelabel{sonata:NoetherianQuotient!for transformation nearrings}{5.5.1}
\makelabel{sonata:CongruenceNoetherianQuotient!for nearrings of polynomial functions}{5.5.2}
\makelabel{sonata:CongruenceNoetherianQuotientForInnerAutomorphismNearRings !for inner automorphism nearrings}{5.5.3}
\makelabel{sonata:Zerosymmetric mappings}{5.6}
\makelabel{sonata:ZeroSymmetricPart!for transformation nearrings}{5.6.1}
\makelabel{sonata:Nearring ideals}{6}
\makelabel{sonata:Construction of nearring ideals}{6.1}
\makelabel{sonata:NearRingIdealByGenerators}{6.1.1}
\makelabel{sonata:NearRingLeftIdealByGenerators}{6.1.2}
\makelabel{sonata:NearRingRightIdealByGenerators}{6.1.3}
\makelabel{sonata:NearRingIdealBySubgroupNC}{6.1.4}
\makelabel{sonata:NearRingLeftIdealBySubgroupNC}{6.1.5}
\makelabel{sonata:NearRingRightIdealBySubgroupNC}{6.1.6}
\makelabel{sonata:NearRingIdeals}{6.1.7}
\makelabel{sonata:NearRingLeftIdeals}{6.1.8}
\makelabel{sonata:NearRingRightIdeals}{6.1.9}
\makelabel{sonata:Testing for ideal properties}{6.2}
\makelabel{sonata:IsNRI}{6.2.1}
\makelabel{sonata:IsNearRingLeftIdeal}{6.2.2}
\makelabel{sonata:IsNearRingRightIdeal}{6.2.3}
\makelabel{sonata:IsNearRingIdeal}{6.2.4}
\makelabel{sonata:IsSubgroupNearRingLeftIdeal}{6.2.5}
\makelabel{sonata:IsSubgroupNearRingRightIdeal}{6.2.6}
\makelabel{sonata:Special ideal properties}{6.3}
\makelabel{sonata:IsPrimeNearRingIdeal}{6.3.1}
\makelabel{sonata:IsMaximalNearRingIdeal}{6.3.2}
\makelabel{sonata:Generators of nearring ideals}{6.4}
\makelabel{sonata:GeneratorsOfNearRingIdeal}{6.4.1}
\makelabel{sonata:GeneratorsOfNearRingLeftIdeal}{6.4.2}
\makelabel{sonata:GeneratorsOfNearRingRightIdeal}{6.4.3}
\makelabel{sonata:Near-ring ideal elements}{6.5}
\makelabel{sonata:AsList!near ring ideals}{6.5.1}
\makelabel{sonata:AsSortedList!near ring ideals}{6.5.2}
\makelabel{sonata:Enumerator!near ring ideals}{6.5.3}
\makelabel{sonata:Random ideal elements}{6.6}
\makelabel{sonata:Random!near ring ideal element}{6.6.1}
\makelabel{sonata:Membership of an ideal}{6.7}
\makelabel{sonata:in}{6.7.1}
\makelabel{sonata:Size of ideals}{6.8}
\makelabel{sonata:Size!near ring ideals}{6.8.1}
\makelabel{sonata:Group reducts of ideals}{6.9}
\makelabel{sonata:GroupReduct!near ring ideals}{6.9.1}
\makelabel{sonata:Comparision of ideals}{6.10}
\makelabel{sonata:=}{6.10.1}
\makelabel{sonata:Operations with ideals}{6.11}
\makelabel{sonata:Intersection!for nearring ideals}{6.11.1}
\makelabel{sonata:Intersection}{6.11.2}
\makelabel{sonata:ClosureNearRingLeftIdeal}{6.11.3}
\makelabel{sonata:ClosureNearRingRightIdeal}{6.11.4}
\makelabel{sonata:ClosureNearRingIdeal}{6.11.5}
\makelabel{sonata:Commutators}{6.12}
\makelabel{sonata:NearRingCommutator}{6.12.1}
\makelabel{sonata:Simple nearrings}{6.13}
\makelabel{sonata:IsSimpleNearRing}{6.13.1}
\makelabel{sonata:Factor nearrings}{6.14}
\makelabel{sonata:FactorNearRing}{6.14.1}
\makelabel{sonata:/}{6.14.2}
\makelabel{sonata:Graphic ideal lattices (X-GAP only)}{7}
\makelabel{sonata:GraphicIdealLattice}{7}
\makelabel{sonata:N-groups}{8}
\makelabel{sonata:Construction of N-groups}{8.1}
\makelabel{sonata:NGroup}{8.1.1}
\makelabel{sonata:NGroupByNearRingMultiplication}{8.1.2}
\makelabel{sonata:NGroupByApplication}{8.1.3}
\makelabel{sonata:NGroupByRightIdealFactor}{8.1.4}
\makelabel{sonata:Operation tables of N-groups}{8.2}
\makelabel{sonata:PrintTable!for N-groups}{8.2.1}
\makelabel{sonata:Functions for N-groups}{8.3}
\makelabel{sonata:IsNGroup}{8.3.1}
\makelabel{sonata:NearRingActingOnNGroup}{8.3.2}
\makelabel{sonata:ActionOfNearRingOnNGroup}{8.3.3}
\makelabel{sonata:N-subgroups}{8.4}
\makelabel{sonata:NSubgroup}{8.4.1}
\makelabel{sonata:NSubgroups}{8.4.2}
\makelabel{sonata:IsNSubgroup}{8.4.3}
\makelabel{sonata:N0-subgroups}{8.5}
\makelabel{sonata:N0Subgroups}{8.5.1}
\makelabel{sonata:Ideals of N-groups}{8.6}
\makelabel{sonata:NIdeal}{8.6.1}
\makelabel{sonata:NIdeals}{8.6.2}
\makelabel{sonata:IsNIdeal}{8.6.3}
\makelabel{sonata:IsSimpleNGroup}{8.6.4}
\makelabel{sonata:IsN0SimpleNGroup}{8.6.5}
\makelabel{sonata:Special properties of N-groups}{8.7}
\makelabel{sonata:IsCompatible}{8.7.1}
\makelabel{sonata:IsTameNGroup}{8.7.2}
\makelabel{sonata:Is2TameNGroup}{8.7.3}
\makelabel{sonata:Is3TameNGroup}{8.7.4}
\makelabel{sonata:IsMonogenic}{8.7.5}
\makelabel{sonata:IsStronglyMonogenic}{8.7.6}
\makelabel{sonata:TypeOfNGroup}{8.7.7}
\makelabel{sonata:Noetherian quotients}{8.8}
\makelabel{sonata:NoetherianQuotient}{8.8.1}
\makelabel{sonata:Nearring radicals}{8.9}
\makelabel{sonata:NuRadical}{8.9.1}
\makelabel{sonata:NuRadicals}{8.9.2}
\makelabel{sonata:Fixed-point-free automorphism groups}{9}
\makelabel{sonata:Fixed-point-free automorphism groups and Frobenius groups}{9.1}
\makelabel{sonata:IsFpfAutomorphismGroup}{9.1.1}
\makelabel{sonata:FpfAutomorphismGroupsMaxSize}{9.1.2}
\makelabel{sonata:FrobeniusGroup}{9.1.3}
\makelabel{sonata:Fixed-point-free representations}{9.2}
\makelabel{sonata:IsFpfRepresentation}{9.2.1}
\makelabel{sonata:DegreeOfIrredFpfRepCyclic}{9.2.2}
\makelabel{sonata:DegreeOfIrredFpfRepMetacyclic}{9.2.3}
\makelabel{sonata:DegreeOfIrredFpfRep2}{9.2.4}
\makelabel{sonata:DegreeOfIrredFpfRep3}{9.2.5}
\makelabel{sonata:DegreeOfIrredFpfRep4}{9.2.6}
\makelabel{sonata:FpfRepresentationsCyclic}{9.2.7}
\makelabel{sonata:FpfRepresentationsMetacyclic}{9.2.8}
\makelabel{sonata:FpfRepresentations2}{9.2.9}
\makelabel{sonata:FpfRepresentations3}{9.2.10}
\makelabel{sonata:FpfRepresentations4}{9.2.11}
\makelabel{sonata:Fixed-point-free automorphism groups}{9.3}
\makelabel{sonata:FpfAutomorphismGroupsCyclic}{9.3.1}
\makelabel{sonata:FpfAutomorphismGroupsMetacyclic}{9.3.2}
\makelabel{sonata:FpfAutomorphismGroups2}{9.3.3}
\makelabel{sonata:FpfAutomorphismGroups3}{9.3.4}
\makelabel{sonata:FpfAutomorphismGroups4}{9.3.5}
\makelabel{sonata:Nearfields, planar nearrings and weakly divisible nearrings}{10}
\makelabel{sonata:Dickson numbers}{10.1}
\makelabel{sonata:IsPairOfDicksonNumbers}{10.1.1}
\makelabel{sonata:Dickson nearfields}{10.2}
\makelabel{sonata:DicksonNearFields}{10.2.1}
\makelabel{sonata:NumberOfDicksonNearFields}{10.2.2}
\makelabel{sonata:Exceptional nearfields}{10.3}
\makelabel{sonata:ExceptionalNearFields}{10.3.1}
\makelabel{sonata:AllExceptionalNearFields}{10.3.2}
\makelabel{sonata:Planar nearrings}{10.4}
\makelabel{sonata:PlanarNearRing}{10.4.1}
\makelabel{sonata:OrbitRepresentativesForPlanarNearRing}{10.4.2}
\makelabel{sonata:Weakly divisible nearrings}{10.5}
\makelabel{sonata:WdNearRing}{10.5.1}
\makelabel{sonata:Designs}{11}
\makelabel{sonata:Constructing a design}{11.1}
\makelabel{sonata:DesignFromPointsAndBlocks}{11.1.1}
\makelabel{sonata:DesignFromIncidenceMat}{11.1.2}
\makelabel{sonata:DesignFromPlanarNearRing}{11.1.3}
\makelabel{sonata:DesignFromFerreroPair}{11.1.4}
\makelabel{sonata:DesignFromWdNearRing}{11.1.5}
\makelabel{sonata:Properties of a design}{11.2}
\makelabel{sonata:PointsOfDesign}{11.2.1}
\makelabel{sonata:BlocksOfDesign}{11.2.2}
\makelabel{sonata:DesignParameter}{11.2.3}
\makelabel{sonata:IncidenceMat}{11.2.4}
\makelabel{sonata:PrintIncidenceMat}{11.2.5}
\makelabel{sonata:BlockIntersectionNumbers}{11.2.6}
\makelabel{sonata:BlockIntersectionNumbersK}{11.2.6}
\makelabel{sonata:IsCircularDesign}{11.2.7}
\makelabel{sonata:Working with the points and blocks of a design}{11.3}
\makelabel{sonata:IsPointIncidentBlock}{11.3.1}
\makelabel{sonata:PointsIncidentBlocks}{11.3.2}
\makelabel{sonata:BlocksIncidentPoints}{11.3.3}
\makelabel{sonata:Bibliography}{}
\setcitlab {aichingereckernoebauer00:TUOCINT}{AEN00}
\setcitlab {aichingerea00:CWN}{Aic00}
\setcitlab {Clay:Nearrings}{Cla92}
\setcitlab {ecker98:OTNOPFONGOC2}{Eck98}
\setcitlab {Mayr:Representations}{May00}
\setcitlab {meldrum85:NATLWG}{Mel85}
\setcitlab {Pilz:Nearrings}{Pil83}
\setcitlab {scott69:TAOPMOAGATSOCPPGI}{Sco69}
\setcitlab {thomaswood80:GT}{TW80}
\setcitlab {Waehling:Fastkoerper}{W{\accent 127 a}h87}
\setcitlab {Wolf:Spaces}{Wol67}
\makelabel{sonata:Index}{}
