\makelabel {sonata:chapter Copyright notice}{2}
\makelabel {sonata:chapter The authors}{3}
\makelabel {sonata:chapter Preface}{4}
\makelabel {sonata:chapter Supportive functions for groups}{1}
\makelabel {sonata:Predefined groups}{1.1}
\makelabel {sonata:TWGroup}{1.1}
\makelabel {sonata:IdTWGroup}{1.1}
\makelabel {sonata:Operation tables for groups}{1.2}
\makelabel {sonata:PrintTable}{1.2}
\makelabel {sonata:Group endomorphisms}{1.3}
\makelabel {sonata:Endomorphisms}{1.3}
\makelabel {sonata:Group automorphisms}{1.4}
\makelabel {sonata:Automorphisms}{1.4}
\makelabel {sonata:Inner automorphisms of a group}{1.5}
\makelabel {sonata:InnerAutomorphisms}{1.5}
\makelabel {sonata:Isomorphic groups}{1.6}
\makelabel {sonata:IsIsomorphicGroup}{1.6}
\makelabel {sonata:Subgroups of a group}{1.7}
\makelabel {sonata:Subgroups}{1.7}
\makelabel {sonata:Normal subgroups generated by a single element}{1.8}
\makelabel {sonata:OneGeneratedNormalSubgroups}{1.8}
\makelabel {sonata:Invariant subgroups}{1.9}
\makelabel {sonata:IsInvariantUnderMaps}{1.9}
\makelabel {sonata:IsCharacteristicSubgroup}{1.9}
\makelabel {sonata:IsCharacteristicInParent}{1.9}
\makelabel {sonata:IsFullinvariant}{1.9}
\makelabel {sonata:IsFullinvariantInParent}{1.9}
\makelabel {sonata:Coset representatives}{1.10}
\makelabel {sonata:RepresentativesModNormalSubgroup}{1.10}
\makelabel {sonata:NontrivialRepresentativesModNormalSubgroup}{1.10}
\makelabel {sonata:Nilpotency class}{1.11}
\makelabel {sonata:NilpotencyClass}{1.11}
\makelabel {sonata:Scott length}{1.12}
\makelabel {sonata:ScottLength}{1.12}
\makelabel {sonata:Other useful functions for groups}{1.13}
\makelabel {sonata:AsPermGroup}{1.13}
\makelabel {sonata:chapter Nearrings}{2}
\makelabel {sonata:Defining a nearring multiplication}{2.1}
\makelabel {sonata:IsNearRingMultiplication}{2.1}
\makelabel {sonata:NearRingMultiplicationByOperationTable}{2.1}
\makelabel {sonata:Construction of nearrings}{2.2}
\makelabel {sonata:ExplicitMultiplicationNearRing}{2.2}
\makelabel {sonata:ExplicitMultiplicationNearRingNC}{2.2}
\makelabel {sonata:IsNearRing}{2.2}
\makelabel {sonata:IsExplicitMultiplicationNearRing}{2.2}
\makelabel {sonata:Direct products of nearrings}{2.3}
\makelabel {sonata:DirectProductNearRing}{2.3}
\makelabel {sonata:Operation tables for nearrings}{2.4}
\makelabel {sonata:PrintTable!near rings}{2.4}
\makelabel {sonata:Modified symbols for the operation tables}{2.5}
\makelabel {sonata:SetSymbols}{2.5}
\makelabel {sonata:SetSymbolsSupervised}{2.5}
\makelabel {sonata:Symbols}{2.5}
\makelabel {sonata:Accessing nearring elements}{2.6}
\makelabel {sonata:AsNearRingElement}{2.6}
\makelabel {sonata:AsGroupReductElement}{2.6}
\makelabel {sonata:Nearring elements}{2.7}
\makelabel {sonata:AsList!near rings}{2.7}
\makelabel {sonata:AsSortedList!near rings}{2.7}
\makelabel {sonata:Enumerator!near rings}{2.7}
\makelabel {sonata:Random nearring elements}{2.8}
\makelabel {sonata:Random!near ring element}{2.8}
\makelabel {sonata:Nearring generators}{2.9}
\makelabel {sonata:GeneratorsOfNearRing}{2.9}
\makelabel {sonata:Size of a nearring}{2.10}
\makelabel {sonata:Size!near rings}{2.10}
\makelabel {sonata:The additive group of a nearring}{2.11}
\makelabel {sonata:GroupReduct}{2.11}
\makelabel {sonata:Nearring endomorphisms}{2.12}
\makelabel {sonata:Endomorphisms!near rings}{2.12}
\makelabel {sonata:Nearring automorphisms}{2.13}
\makelabel {sonata:Automorphisms!near rings}{2.13}
\makelabel {sonata:Isomorphic nearrings}{2.14}
\makelabel {sonata:IsIsomorphicNearRing}{2.14}
\makelabel {sonata:Subnearrings}{2.15}
\makelabel {sonata:SubNearRings}{2.15}
\makelabel {sonata:Invariant subnearrings}{2.16}
\makelabel {sonata:InvariantSubNearRings}{2.16}
\makelabel {sonata:Constructing subnearrings}{2.17}
\makelabel {sonata:SubNearRingBySubgroupNC}{2.17}
\makelabel {sonata:Intersection of nearrings}{2.18}
\makelabel {sonata:Intersection!for nearrings}{2.18}
\makelabel {sonata:Identity of a nearring}{2.19}
\makelabel {sonata:Identity}{2.19}
\makelabel {sonata:One}{2.19}
\makelabel {sonata:IsNearRingWithOne}{2.19}
\makelabel {sonata:Units of a nearring}{2.20}
\makelabel {sonata:IsNearRingUnit}{2.20}
\makelabel {sonata:NearRingUnits}{2.20}
\makelabel {sonata:Distributivity in a nearring}{2.21}
\makelabel {sonata:Distributors}{2.21}
\makelabel {sonata:DistributiveElements}{2.21}
\makelabel {sonata:IsDistributiveNearRing}{2.21}
\makelabel {sonata:Elements of a nearring with special properties}{2.22}
\makelabel {sonata:ZeroSymmetricElements}{2.22}
\makelabel {sonata:IdempotentElements}{2.22}
\makelabel {sonata:NilpotentElements}{2.22}
\makelabel {sonata:QuasiregularElements}{2.22}
\makelabel {sonata:RegularElements}{2.22}
\makelabel {sonata:Special properties of a nearring}{2.23}
\makelabel {sonata:IsAbelianNearRing}{2.23}
\makelabel {sonata:IsAbstractAffineNearRing}{2.23}
\makelabel {sonata:IsBooleanNearRing}{2.23}
\makelabel {sonata:IsNilNearRing}{2.23}
\makelabel {sonata:IsNilpotentNearRing}{2.23}
\makelabel {sonata:IsNilpotentFreeNearRing}{2.23}
\makelabel {sonata:IsCommutative}{2.23}
\makelabel {sonata:IsDgNearRing}{2.23}
\makelabel {sonata:IsIntegralNearRing}{2.23}
\makelabel {sonata:IsPrimeNearRing}{2.23}
\makelabel {sonata:IsQuasiregularNearRing}{2.23}
\makelabel {sonata:IsRegularNearRing}{2.23}
\makelabel {sonata:IsNearField}{2.23}
\makelabel {sonata:IsPlanarNearRing}{2.23}
\makelabel {sonata:IsWdNearRing}{2.23}
\makelabel {sonata:chapter The nearring library}{3}
\makelabel {sonata:Extracting nearrings from the library}{3.1}
\makelabel {sonata:LibraryNearRing}{3.1}
\makelabel {sonata:NumberLibraryNearRings}{3.1}
\makelabel {sonata:AllLibraryNearRings}{3.1}
\makelabel {sonata:LibraryNearRingWithOne}{3.1}
\makelabel {sonata:NumberLibraryNearRingsWithOne}{3.1}
\makelabel {sonata:AllLibraryNearRingsWithOne}{3.1}
\makelabel {sonata:Identifying nearrings}{3.2}
\makelabel {sonata:IdLibraryNearRing}{3.2}
\makelabel {sonata:IdLibraryNearRingWithOne}{3.2}
\makelabel {sonata:IsLibraryNearRing}{3.3}
\makelabel {sonata:IsLibraryNearRing}{3.3}
\makelabel {sonata:Accessing the information about a nearring stored in the library}{3.4}
\makelabel {sonata:LibraryNearRingInfo}{3.4}
\makelabel {sonata:chapter Arbitrary functions on groups: EndoMappings}{4}
\makelabel {sonata:Defining endo mappings}{4.1}
\makelabel {sonata:EndoMappingByPositionList }{4.1}
\makelabel {sonata:EndoMappingByFunction}{4.1}
\makelabel {sonata:AsEndoMapping}{4.1}
\makelabel {sonata:AsGroupGeneralMappingByImages}{4.1}
\makelabel {sonata:IsEndoMapping}{4.1}
\makelabel {sonata:IdentityEndoMapping}{4.1}
\makelabel {sonata:ConstantEndoMapping}{4.1}
\makelabel {sonata:Properties of endo mappings}{4.2}
\makelabel {sonata:IsIdentityEndoMapping}{4.2}
\makelabel {sonata:IsConstantEndoMapping}{4.2}
\makelabel {sonata:IsDistributiveEndoMapping}{4.2}
\makelabel {sonata:Operations for endo mappings}{4.3}
\makelabel {sonata:Nicer ways to print a mapping}{4.4}
\makelabel {sonata:GraphOfMapping}{4.4}
\makelabel {sonata:PrintAsTerm}{4.4}
\makelabel {sonata:chapter Transformation nearrings}{5}
\makelabel {sonata:Constructing transformation nearrings}{5.1}
\makelabel {sonata:TransformationNearRingByGenerators}{5.1}
\makelabel {sonata:TransformationNearRingByAdditiveGenerators}{5.1}
\makelabel {sonata:Nearrings of transformations}{5.2}
\makelabel {sonata:MapNearRing}{5.2}
\makelabel {sonata:TransformationNearRing}{5.2}
\makelabel {sonata:IsFullTransformationNearRing}{5.2}
\makelabel {sonata:PolynomialNearRing}{5.2}
\makelabel {sonata:EndomorphismNearRing}{5.2}
\makelabel {sonata:AutomorphismNearRing}{5.2}
\makelabel {sonata:InnerAutomorphismNearRing}{5.2}
\makelabel {sonata:CompatibleFunctionNearRing}{5.2}
\makelabel {sonata:ZeroSymmetricCompatibleFunctionNearRing}{5.2}
\makelabel {sonata:IsCompatibleEndoMapping}{5.2}
\makelabel {sonata:Is1AffineComplete}{5.2}
\makelabel {sonata:CentralizerNearRing}{5.2}
\makelabel {sonata:RestrictedEndomorphismNearRing}{5.2}
\makelabel {sonata:LocalInterpolationNearRing}{5.2}
\makelabel {sonata:The group a transformation nearring acts on}{5.3}
\makelabel {sonata:Gamma}{5.3}
\makelabel {sonata:Transformation nearrings and other nearrings}{5.4}
\makelabel {sonata:AsTransformationNearRing}{5.4}
\makelabel {sonata:AsExplicitMultiplicationNearRing}{5.4}
\makelabel {sonata:Noetherian quotients for transformation nearrings}{5.5}
\makelabel {sonata:NoetherianQuotient!for transformation nearrings}{5.5}
\makelabel {sonata:CongruenceNoetherianQuotient!for nearrings of polynomial functions}{5.5}
\makelabel {sonata:CongruenceNoetherianQuotientForInnerAutomorphismNearRings !for inner automorphism nearrings}{5.5}
\makelabel {sonata:Zerosymmetric mappings}{5.6}
\makelabel {sonata:ZeroSymmetricPart!for transformation nearrings}{5.6}
\makelabel {sonata:chapter Nearring ideals}{6}
\makelabel {sonata:Construction of nearring ideals}{6.1}
\makelabel {sonata:NearRingIdealByGenerators}{6.1}
\makelabel {sonata:NearRingLeftIdealByGenerators}{6.1}
\makelabel {sonata:NearRingRightIdealByGenerators}{6.1}
\makelabel {sonata:NearRingIdealBySubgroupNC}{6.1}
\makelabel {sonata:NearRingLeftIdealBySubgroupNC}{6.1}
\makelabel {sonata:NearRingRightIdealBySubgroupNC}{6.1}
\makelabel {sonata:NearRingIdeals}{6.1}
\makelabel {sonata:NearRingLeftIdeals}{6.1}
\makelabel {sonata:NearRingRightIdeals}{6.1}
\makelabel {sonata:Testing for ideal properties}{6.2}
\makelabel {sonata:IsNRI}{6.2}
\makelabel {sonata:IsNearRingLeftIdeal}{6.2}
\makelabel {sonata:IsNearRingRightIdeal}{6.2}
\makelabel {sonata:IsNearRingIdeal}{6.2}
\makelabel {sonata:IsSubgroupNearRingLeftIdeal}{6.2}
\makelabel {sonata:IsSubgroupNearRingRightIdeal}{6.2}
\makelabel {sonata:Special ideal properties}{6.3}
\makelabel {sonata:IsPrimeNearRingIdeal}{6.3}
\makelabel {sonata:IsMaximalNearRingIdeal}{6.3}
\makelabel {sonata:Generators of nearring ideals}{6.4}
\makelabel {sonata:GeneratorsOfNearRingIdeal}{6.4}
\makelabel {sonata:GeneratorsOfNearRingLeftIdeal}{6.4}
\makelabel {sonata:GeneratorsOfNearRingRightIdeal}{6.4}
\makelabel {sonata:Near-ring ideal elements}{6.5}
\makelabel {sonata:AsList!near ring ideals}{6.5}
\makelabel {sonata:AsSortedList!near ring ideals}{6.5}
\makelabel {sonata:Enumerator!near ring ideals}{6.5}
\makelabel {sonata:Random ideal elements}{6.6}
\makelabel {sonata:Random!near ring ideal element}{6.6}
\makelabel {sonata:Membership of an ideal}{6.7}
\makelabel {sonata:in}{6.7}
\makelabel {sonata:Size of ideals}{6.8}
\makelabel {sonata:Size!near ring ideals}{6.8}
\makelabel {sonata:Group reducts of ideals}{6.9}
\makelabel {sonata:GroupReduct!near ring ideals}{6.9}
\makelabel {sonata:Comparision of ideals}{6.10}
\makelabel {sonata:=}{6.10}
\makelabel {sonata:Operations with ideals}{6.11}
\makelabel {sonata:Intersection!for nearring ideals}{6.11}
\makelabel {sonata:Intersection}{6.11}
\makelabel {sonata:ClosureNearRingLeftIdeal}{6.11}
\makelabel {sonata:ClosureNearRingRightIdeal}{6.11}
\makelabel {sonata:ClosureNearRingIdeal}{6.11}
\makelabel {sonata:Commutators}{6.12}
\makelabel {sonata:NearRingCommutator}{6.12}
\makelabel {sonata:Simple nearrings}{6.13}
\makelabel {sonata:IsSimpleNearRing}{6.13}
\makelabel {sonata:Factor nearrings}{6.14}
\makelabel {sonata:FactorNearRing}{6.14}
\makelabel {sonata:/}{6.14}
\makelabel {sonata:chapter Graphic ideal lattices (X-GAP only)}{7}
\makelabel {sonata:GraphicIdealLattice}{7}
\makelabel {sonata:chapter N-groups}{8}
\makelabel {sonata:Construction of N-groups}{8.1}
\makelabel {sonata:NGroup}{8.1}
\makelabel {sonata:NGroupByNearRingMultiplication}{8.1}
\makelabel {sonata:NGroupByApplication}{8.1}
\makelabel {sonata:NGroupByRightIdealFactor}{8.1}
\makelabel {sonata:Operation tables of N-groups}{8.2}
\makelabel {sonata:PrintTable!for N-groups}{8.2}
\makelabel {sonata:Functions for N-groups}{8.3}
\makelabel {sonata:IsNGroup}{8.3}
\makelabel {sonata:NearRingActingOnNGroup}{8.3}
\makelabel {sonata:ActionOfNearRingOnNGroup}{8.3}
\makelabel {sonata:N-subgroups}{8.4}
\makelabel {sonata:NSubgroup}{8.4}
\makelabel {sonata:NSubgroups}{8.4}
\makelabel {sonata:IsNSubgroup}{8.4}
\makelabel {sonata:N0-subgroups}{8.5}
\makelabel {sonata:N0Subgroups}{8.5}
\makelabel {sonata:Ideals of N-groups}{8.6}
\makelabel {sonata:NIdeal}{8.6}
\makelabel {sonata:NIdeals}{8.6}
\makelabel {sonata:IsNIdeal}{8.6}
\makelabel {sonata:IsSimpleNGroup}{8.6}
\makelabel {sonata:IsN0SimpleNGroup}{8.6}
\makelabel {sonata:Special properties of N-groups}{8.7}
\makelabel {sonata:IsCompatible}{8.7}
\makelabel {sonata:IsTameNGroup}{8.7}
\makelabel {sonata:Is2TameNGroup}{8.7}
\makelabel {sonata:Is3TameNGroup}{8.7}
\makelabel {sonata:IsMonogenic}{8.7}
\makelabel {sonata:IsStronglyMonogenic}{8.7}
\makelabel {sonata:TypeOfNGroup}{8.7}
\makelabel {sonata:Noetherian quotients}{8.8}
\makelabel {sonata:NoetherianQuotient}{8.8}
\makelabel {sonata:Nearring radicals}{8.9}
\makelabel {sonata:NuRadical}{8.9}
\makelabel {sonata:NuRadicals}{8.9}
\makelabel {sonata:chapter Fixed-point-free automorphism groups}{9}
\makelabel {sonata:Fixed-point-free automorphism groups and Frobenius groups}{9.1}
\makelabel {sonata:IsFpfAutomorphismGroup}{9.1}
\makelabel {sonata:FpfAutomorphismGroupsMaxSize}{9.1}
\makelabel {sonata:FrobeniusGroup}{9.1}
\makelabel {sonata:Fixed-point-free representations}{9.2}
\makelabel {sonata:IsFpfRepresentation}{9.2}
\makelabel {sonata:DegreeOfIrredFpfRepCyclic}{9.2}
\makelabel {sonata:DegreeOfIrredFpfRepMetacyclic}{9.2}
\makelabel {sonata:DegreeOfIrredFpfRep2}{9.2}
\makelabel {sonata:DegreeOfIrredFpfRep3}{9.2}
\makelabel {sonata:DegreeOfIrredFpfRep4}{9.2}
\makelabel {sonata:FpfRepresentationsCyclic}{9.2}
\makelabel {sonata:FpfRepresentationsMetacyclic}{9.2}
\makelabel {sonata:FpfRepresentations2}{9.2}
\makelabel {sonata:FpfRepresentations3}{9.2}
\makelabel {sonata:FpfRepresentations4}{9.2}
\makelabel {sonata:Fixed-point-free automorphism groups}{9.3}
\makelabel {sonata:FpfAutomorphismGroupsCyclic}{9.3}
\makelabel {sonata:FpfAutomorphismGroupsMetacyclic}{9.3}
\makelabel {sonata:FpfAutomorphismGroups2}{9.3}
\makelabel {sonata:FpfAutomorphismGroups3}{9.3}
\makelabel {sonata:FpfAutomorphismGroups4}{9.3}
\makelabel {sonata:chapter Nearfields, planar nearrings and weakly divisible nearrings}{10}
\makelabel {sonata:Dickson numbers}{10.1}
\makelabel {sonata:IsPairOfDicksonNumbers}{10.1}
\makelabel {sonata:Dickson nearfields}{10.2}
\makelabel {sonata:DicksonNearFields}{10.2}
\makelabel {sonata:NumberOfDicksonNearFields}{10.2}
\makelabel {sonata:Exceptional nearfields}{10.3}
\makelabel {sonata:ExceptionalNearFields}{10.3}
\makelabel {sonata:AllExceptionalNearFields}{10.3}
\makelabel {sonata:Planar nearrings}{10.4}
\makelabel {sonata:PlanarNearRing}{10.4}
\makelabel {sonata:OrbitRepresentativesForPlanarNearRing}{10.4}
\makelabel {sonata:Weakly divisible nearrings}{10.5}
\makelabel {sonata:WdNearRing}{10.5}
\makelabel {sonata:chapter Designs}{11}
\makelabel {sonata:Constructing a design}{11.1}
\makelabel {sonata:DesignFromPointsAndBlocks}{11.1}
\makelabel {sonata:DesignFromIncidenceMat}{11.1}
\makelabel {sonata:DesignFromPlanarNearRing}{11.1}
\makelabel {sonata:DesignFromFerreroPair}{11.1}
\makelabel {sonata:DesignFromWdNearRing}{11.1}
\makelabel {sonata:Properties of a design}{11.2}
\makelabel {sonata:PointsOfDesign}{11.2}
\makelabel {sonata:BlocksOfDesign}{11.2}
\makelabel {sonata:DesignParameter}{11.2}
\makelabel {sonata:IncidenceMat}{11.2}
\makelabel {sonata:PrintIncidenceMat}{11.2}
\makelabel {sonata:BlockIntersectionNumbers}{11.2}
\makelabel {sonata:BlockIntersectionNumbersK}{11.2}
\makelabel {sonata:IsCircularDesign}{11.2}
\makelabel {sonata:Working with the points and blocks of a design}{11.3}
\makelabel {sonata:IsPointIncidentBlock}{11.3}
\makelabel {sonata:PointsIncidentBlocks}{11.3}
\makelabel {sonata:BlocksIncidentPoints}{11.3}
\makelabel {sonata:chapter Bibliography}{1}
\makelabel {sonata:chapter Index}{2}
