# SONATA : a GAP 4 package - Index

_ A B C D E F G I L M N O P Q R S T U W Z

## _

/ 6.14.2
= 6.10.1

## A

Accessing nearring elements 2.6
Accessing the information about a nearring stored in the library 3.4
ActionOfNearRingOnNGroup 8.3.3
AllExceptionalNearFields 10.3.2
AllLibraryNearRings 3.1.3
AllLibraryNearRingsWithOne 3.1.6
Arbitrary functions on groups: EndoMappings 4.0
AsEndoMapping 4.1.3
AsExplicitMultiplicationNearRing 5.4.2
AsGroupGeneralMappingByImages 4.1.4
AsGroupReductElement 2.6.2
AsList, near ring ideals 6.5.1
AsList, near rings 2.7.1
AsNearRingElement 2.6.1
AsPermGroup 1.12.1
AsSortedList, near ring ideals 6.5.2
AsSortedList, near rings 2.7.2
AsTransformationNearRing 5.4.1
AutomorphismNearRing 5.2.6
Automorphisms 1.4.1
Automorphisms, near rings 2.13.1

## B

BlockIntersectionNumbers 11.2.6
BlockIntersectionNumbersK 11.2.6
BlocksIncidentPoints 11.3.3
BlocksOfDesign 11.2.2

## C

CentralizerNearRing 5.2.12
ClosureNearRingIdeal 6.11.5
ClosureNearRingLeftIdeal 6.11.3
ClosureNearRingRightIdeal 6.11.4
Commutators 6.12
Comparision of ideals 6.10
CompatibleFunctionNearRing 5.2.8
CongruenceNoetherianQuotient, for nearrings of polynomial functions 5.5.2
CongruenceNoetherianQuotientForInnerAutomorphismNearRings , for inner automorphism nearrings 5.5.3
ConstantEndoMapping 4.1.7
Constructing a design 11.1
Constructing subnearrings 2.17
Constructing transformation nearrings 5.1
Construction of N-groups 8.1
Construction of nearring ideals 6.1
Construction of nearrings 2.2
Coset representatives 1.10

## D

Defining a nearring multiplication 2.1
Defining endo mappings 4.1
DegreeOfIrredFpfRep2 9.2.4
DegreeOfIrredFpfRep3 9.2.5
DegreeOfIrredFpfRep4 9.2.6
DegreeOfIrredFpfRepCyclic 9.2.2
DegreeOfIrredFpfRepMetacyclic 9.2.3
DesignFromFerreroPair 11.1.4
DesignFromIncidenceMat 11.1.2
DesignFromPlanarNearRing 11.1.3
DesignFromPointsAndBlocks 11.1.1
DesignFromWdNearRing 11.1.5
DesignParameter 11.2.3
Designs 11.0
Dickson nearfields 10.2
Dickson numbers 10.1
DicksonNearFields 10.2.1
Direct products of nearrings 2.3
DirectProductNearRing 2.3.1
DistributiveElements 2.21.2
Distributivity in a nearring 2.21
Distributors 2.21.1

## E

Elements of a nearring with special properties 2.22
EndoMappingByFunction 4.1.2
EndoMappingByPositionList 4.1.1
EndomorphismNearRing 5.2.5
Endomorphisms 1.3.1
Endomorphisms, near rings 2.12.1
Enumerator, near ring ideals 6.5.3
Enumerator, near rings 2.7.3
Exceptional nearfields 10.3
ExceptionalNearFields 10.3.1
ExplicitMultiplicationNearRing 2.2.1
ExplicitMultiplicationNearRingNC 2.2.2
Extracting nearrings from the library 3.1

## F

Factor nearrings 6.14
FactorNearRing 6.14.1
Fixed-point-free automorphism groups 9.0 9.3
Fixed-point-free automorphism groups and Frobenius groups 9.1
Fixed-point-free representations 9.2
FpfAutomorphismGroups2 9.3.3
FpfAutomorphismGroups3 9.3.4
FpfAutomorphismGroups4 9.3.5
FpfAutomorphismGroupsCyclic 9.3.1
FpfAutomorphismGroupsMaxSize 9.1.2
FpfAutomorphismGroupsMetacyclic 9.3.2
FpfRepresentations2 9.2.9
FpfRepresentations3 9.2.10
FpfRepresentations4 9.2.11
FpfRepresentationsCyclic 9.2.7
FpfRepresentationsMetacyclic 9.2.8
FrobeniusGroup 9.1.3
Functions for N-groups 8.3

## G

Gamma 5.3.1
Generators of nearring ideals 6.4
GeneratorsOfNearRing 2.9.1
GeneratorsOfNearRingIdeal 6.4.1
GeneratorsOfNearRingLeftIdeal 6.4.2
GeneratorsOfNearRingRightIdeal 6.4.3
Graphic ideal lattices (XGAP only) 7.0
GraphicIdealLattice 7.0
GraphOfMapping 4.4.1
Group automorphisms 1.4
Group endomorphisms 1.3
Group reducts of ideals 6.9
GroupReduct 2.11.1
GroupReduct, near ring ideals 6.9.1

## I

Ideals of N-groups 8.6
IdempotentElements 2.22.2
Identifying nearrings 3.2
Identity 2.19.1
Identity of a nearring 2.19
IdentityEndoMapping 4.1.6
IdLibraryNearRing 3.2.1
IdLibraryNearRingWithOne 3.2.2
IdTWGroup 1.1.2
in 6.7.1
IncidenceMat 11.2.4
Inner automorphisms of a group 1.5
InnerAutomorphismNearRing 5.2.7
InnerAutomorphisms 1.5.1
Intersection 6.11.2
Intersection of nearrings 2.18
Intersection, for nearring ideals 6.11.1
Intersection, for nearrings 2.18.1
Invariant subgroups 1.9
Invariant subnearrings 2.16
InvariantSubNearRings 2.16.1
Is1AffineComplete 5.2.11
Is2TameNGroup 8.7.3
Is3TameNGroup 8.7.4
IsAbelianNearRing 2.23.1
IsAbstractAffineNearRing 2.23.2
IsBooleanNearRing 2.23.3
IsCharacteristicInParent 1.9.3
IsCharacteristicSubgroup 1.9.2
IsCircularDesign 11.2.7
IsCommutative 2.23.7
IsCompatible 8.7.1
IsCompatibleEndoMapping 5.2.10
IsConstantEndoMapping 4.2.2
IsDgNearRing 2.23.8
IsDistributiveEndoMapping 4.2.3
IsDistributiveNearRing 2.21.3
IsEndoMapping 4.1.5
IsExplicitMultiplicationNearRing 2.2.4
IsFpfAutomorphismGroup 9.1.1
IsFpfRepresentation 9.2.1
IsFullinvariant 1.9.4
IsFullinvariantInParent 1.9.5
IsFullTransformationNearRing 5.2.3
IsIdentityEndoMapping 4.2.1
IsIntegralNearRing 2.23.9
IsInvariantUnderMaps 1.9.1
IsIsomorphicGroup 1.6.1
IsIsomorphicNearRing 2.14.1
IsLibraryNearRing 3.3 3.3.1
IsMaximalNearRingIdeal 6.3.2
IsMonogenic 8.7.5
IsN0SimpleNGroup 8.6.5
IsNearField 2.23.13
IsNearRing 2.2.3
IsNearRingIdeal 6.2.4
IsNearRingLeftIdeal 6.2.2
IsNearRingMultiplication 2.1.1
IsNearRingRightIdeal 6.2.3
IsNearRingUnit 2.20.1
IsNearRingWithOne 2.19.3
IsNGroup 8.3.1
IsNIdeal 8.6.3
IsNilNearRing 2.23.4
IsNilpotentFreeNearRing 2.23.6
IsNilpotentNearRing 2.23.5
IsNRI 6.2.1
IsNSubgroup 8.4.3
Isomorphic groups 1.6
Isomorphic nearrings 2.14
IsPairOfDicksonNumbers 10.1.1
IsPlanarNearRing 2.23.14
IsPointIncidentBlock 11.3.1
IsPrimeNearRing 2.23.10
IsPrimeNearRingIdeal 6.3.1
IsQuasiregularNearRing 2.23.11
IsRegularNearRing 2.23.12
IsSimpleNearRing 6.13.1
IsSimpleNGroup 8.6.4
IsStronglyMonogenic 8.7.6
IsSubgroupNearRingLeftIdeal 6.2.5
IsSubgroupNearRingRightIdeal 6.2.6
IsTameNGroup 8.7.2
IsWdNearRing 2.23.15

## L

LibraryNearRing 3.1.1
LibraryNearRingInfo 3.4.1
LibraryNearRingWithOne 3.1.4
LocalInterpolationNearRing 5.2.14

## M

MapNearRing 5.2.1
Membership of an ideal 6.7
Modified symbols for the operation tables 2.5

## N

N-groups 8.0
N-subgroups 8.4
N0-subgroups 8.5
N0Subgroups 8.5.1
Near-ring ideal elements 6.5
Nearfields, planar nearrings and weakly divisible nearrings 10.0
Nearring automorphisms 2.13
Nearring elements 2.7
Nearring endomorphisms 2.12
Nearring generators 2.9
Nearring ideals 6.0
Nearring radicals 8.9
NearRingActingOnNGroup 8.3.2
NearRingCommutator 6.12.1
NearRingIdealByGenerators 6.1.1
NearRingIdealBySubgroupNC 6.1.4
NearRingIdeals 6.1.7
NearRingLeftIdealByGenerators 6.1.2
NearRingLeftIdealBySubgroupNC 6.1.5
NearRingLeftIdeals 6.1.8
NearRingMultiplicationByOperationTable 2.1.2
NearRingRightIdealByGenerators 6.1.3
NearRingRightIdealBySubgroupNC 6.1.6
NearRingRightIdeals 6.1.9
Nearrings 2.0
Nearrings of transformations 5.2
NearRingUnits 2.20.2
NGroup 8.1.1
NGroupByApplication 8.1.3
NGroupByNearRingMultiplication 8.1.2
NGroupByRightIdealFactor 8.1.4
Nicer ways to print a mapping 4.4
NIdeal 8.6.1
NIdeals 8.6.2
NilpotentElements 2.22.3
Noetherian quotients 8.8
Noetherian quotients for transformation nearrings 5.5
NoetherianQuotient 8.8.1
NoetherianQuotient, for transformation nearrings 5.5.1
NontrivialRepresentativesModNormalSubgroup 1.10.2
Normal subgroups generated by a single element 1.8
NSubgroup 8.4.1
NSubgroups 8.4.2
NumberLibraryNearRings 3.1.2
NumberLibraryNearRingsWithOne 3.1.5
NumberOfDicksonNearFields 10.2.2
NuRadical 8.9.1
NuRadicals 8.9.2

## O

One 2.19.2
OneGeneratedNormalSubgroups 1.8.1
Operation tables for groups 1.2
Operation tables for nearrings 2.4
Operation tables of N-groups 8.2
Operations for endo mappings 4.3
Operations with ideals 6.11
OrbitRepresentativesForPlanarNearRing 10.4.2
Other useful functions for groups 1.12

## P

Planar nearrings 10.4
PlanarNearRing 10.4.1
PointsIncidentBlocks 11.3.2
PointsOfDesign 11.2.1
PolynomialNearRing 5.2.4
Predefined groups 1.1
PrintAsTerm 4.4.2
PrintIncidenceMat 11.2.5
PrintTable 1.2.1
PrintTable, for N-groups 8.2.1
PrintTable, near rings 2.4.1
Properties of a design 11.2
Properties of endo mappings 4.2

## Q

QuasiregularElements 2.22.4

## R

Random ideal elements 6.6
Random nearring elements 2.8
Random, near ring element 2.8.1
Random, near ring ideal element 6.6.1
RegularElements 2.22.5
RepresentativesModNormalSubgroup 1.10.1
RestrictedEndomorphismNearRing 5.2.13

## S

Scott length 1.11
ScottLength 1.11.1
SetSymbols 2.5.1
SetSymbolsSupervised 2.5.1
Simple nearrings 6.13
Size of a nearring 2.10
Size of ideals 6.8
Size, near ring ideals 6.8.1
Size, near rings 2.10.1
Special ideal properties 6.3
Special properties of a nearring 2.23
Special properties of N-groups 8.7
Subgroups 1.7.1
Subgroups of a group 1.7
SubNearRingBySubgroupNC 2.17.1
SubNearRings 2.15.1
Subnearrings 2.15
Supportive functions for groups 1.0
Symbols 2.5.2

## T

Testing for ideal properties 6.2
The additive group of a nearring 2.11
The group a transformation nearring acts on 5.3
The nearring library 3.0
Transformation nearrings 5.0
Transformation nearrings and other nearrings 5.4
TransformationNearRing 5.2.2
TransformationNearRingByAdditiveGenerators 5.1.2
TransformationNearRingByGenerators 5.1.1
TWGroup 1.1.1
TypeOfNGroup 8.7.7

## U

Units of a nearring 2.20

## W

WdNearRing 10.5.1
Weakly divisible nearrings 10.5
Working with the points and blocks of a design 11.3

## Z

Zerosymmetric mappings 5.6
ZeroSymmetricCompatibleFunctionNearRing 5.2.9
ZeroSymmetricElements 2.22.1
ZeroSymmetricPart, for transformation nearrings 5.6.1

[Up]