# CRISP : a GAP 4 package - Index

A B C D E F G H I L M N O P R S T U V

## A

abelian groups of bounded exponent, class of 6.1
abelian groups, class of 6.1
AbelianGroups 6.1
AbelianGroupsOfExponent 6.1.5 6.1
AbelianMinimalNormalSubgroups 7.1.5
AbelianSocle 7.2.2
AbelianSocleComponents 7.2.4
Additional attributes for primitive soluble groups 4.3
Additional properties of group classes 3.3
AllInvariantSubgroupsWithNProperty 5.5.2
AllInvariantSubgroupsWithQProperty 4.6.2
AllNormalSubgroupsWithNProperty 5.5.3
AllNormalSubgroupsWithQProperty 4.6.4
AllPrimes 6.3
Attributes and operations for Fitting classes and Fitting sets 5.4
Attributes and operations for formations 4.5
Attributes and operations for Schunck classes 4.2
Attributes of group classes 3.4
attributes, of Fitting classes 5.4
attributes, of Fitting sets 5.4
attributes, of formation 4.5
attributes, of group classes 3.4
attributes, of primitive soluble group 4.3
attributes, of Schunck class 4.2

## B

Basis 4.2.2
Boundary 4.2.1
BoundaryFunction 4.2.5

## C

Carter subgroup 6.2
Characteristic 3.4.1
CharacteristicSubgroups 7.1.2
Class 2.1.2
class, of all abelian groups 6.1.4 6.1
class, of all abelian groups of bounded exponent 6.1
class, of all nilpotent groups 6.1.2 6.1
class, of all p-groups 6.1
class, of all pi-groups 6.1
class, of all supersoluble groups 6.1.3 6.1
class, of all trivial groups 6.1.1 6.1
classes, creation of 2.1
classes, properties of 2.2
closure properties, of group classes 3.2
comparison, for classes 2.1.8
Complement 2.3.1
ContainsTrivialGroup 3.2.2
CoveringSubgroup 4.2.4
Creating Fitting classes 5.1
Creating Fitting formations 5.2
Creating Fitting sets 5.3
Creating formations 4.4
Creating group classes 3.1
Creating Schunck classes 4.1
Creating set theoretical classes 2.1

## D

Difference 2.3.4
Display, for classes 2.1.5

## E

element test, for classes 2.1.6
equality, for classes 2.1.7
Examples of group classes 6.0

## F

Fitting classes and Fitting sets 5.0
Fitting classes, attributes of 5.4
Fitting classes, creating 5.1
Fitting classes, creating Fitting formations 5.2
Fitting classes, operations for 5.4
Fitting formations, creating 5.2
Fitting sets, attributes of 5.4
Fitting sets, creating 5.3
Fitting sets, operations for 5.4
FittingClass 5.1.1
FittingFormation 5.2.1
FittingFormationProduct 4.4.4
FittingProduct 5.1.2
FittingSet 5.3.2
FormationProduct 4.4.3
formations, attributes for 4.5
formations, creating 4.4
formations, creating Fitting formations 5.2
formations, operations for 4.5
Functions for normal and characteristic subgroups 7.1
Functions for the socle of finite groups 7.2

## G

Generic group classes 3.0
group classes, attributes for 3.4
group classes, closure properties of 3.2
group classes, creation of 3.1
group classes, properties of 3.3
GroupClass 3.1.1

## H

HasIsFittingClass 3.3.1
HasIsFittingFormation 3.3.10
HasIsFormation 3.3
HasIsOrdinaryFormation 3.3.4
HasIsSaturatedFittingFormation 3.3.13
HasIsSaturatedFormation 3.3.7

## I

ImageFittingSet 5.3.3
in, for classes 2.1
Injector 5.4.2
InjectorFunction 5.4.4
Intersection, of classes 2.3.2
Intersection, of Fitting sets 5.3.5
Intersection, of group classes 3.1.2
INTERSECTIONnoexpand_LIMIT 2.3
Introduction 1.0
invariant normal subgroups, with properties inherited by normal subgroups 5.5
invariant normal subgroups, with properties inherited by normal subgroups above 4.6
IsClass 2.1.1
IsDirectProductClosed 3.2.8
IsEmpty, for classes 2.2.1
IsFittingClass 3.3.2
IsFittingFormation 3.3.11
IsFittingSet 5.3.1
IsFormation 3.3
IsGroupClass 3.2.1
IsNormalProductClosed 3.2.7
IsNormalSubgroupClosed 3.2.4
IsOrdinaryFormation 3.3.5
IsPrimitiveSoluble 4.3.1
IsPrimitiveSolubleGroup 4.3.1
IsPrimitiveSolvable 4.3.1
IsPrimitiveSolvableGroup 4.3.1
IsQuotientClosed 3.2.5
IsResiduallyClosed 3.2.6
IsSaturated 3.2.10
IsSaturatedFittingFormation 3.3.14
IsSaturatedFormation 3.3.8
IsSchunckClass 3.2.9
IsSubgroupClosed 3.2.3

## L

Lattice operations for classes 2.3
lattice operations, for classes 2.3
Lists of normal subgroups 7.0
LocalDefinitionFunction 4.5.3
Low level functions for normal subgroups related to radicals 5.5
Low level functions for normal subgroups related to residuals 4.6

## M

MemberFunction 2.2.2
membership test, for classes 2.1
minimal normal p-subgroups 7.1
minimal normal subgroups 7.1
MinimalNormalPSubgroups 7.1.4
MinimalNormalSubgroups 7.1.3

## N

nilpotent groups, class of 6.1
NilpotentGroups 6.1
NilpotentProjector 6.2.1
normal subgroups, with properties inherited by factor groups 4.6
normal subgroups, with properties inherited by normal subgroups 5.5
normal subgroups, with properties inherited by normal subgroups above 4.6
normal subgroups, with properties inherited by quotients 4.6
NormalSubgroups 7.1.1

## O

OneInvariantSubgroupMaxWrtNProperty 5.5.1
OneInvariantSubgroupMinWrtQProperty 4.6.1
OneNormalSubgroupMinWrtQProperty 4.6.3
OneNormalSubgroupWithNProperty 5.5.3
operations, for Fitting classes 5.4
operations, for Fitting sets 5.4
operations, for formation 4.5
operations, for Schunck class, 4.2
OrdinaryFormation 4.4.1

## P

PGroups 6.1.7
PiGroups 6.1.6
Pre-defined group classes 6.1
Pre-defined projector functions 6.2
Pre-defined sets of primes 6.3
PreImageFittingSet 5.3.4
primes, set of all 6.3
primitive soluble group, attributes of 4.3
Print, for classes 2.1.4
Projector 4.2.3
ProjectorFunction 4.2.6
Properties of classes 2.2
Properties of group classes 3.2
properties, of classes 2.2
properties, of group classes 3.3
PSocle 7.2.5
PSocleComponents 7.2.6
PSocleSeries 7.2.7

## R

Radical 5.4.1
RadicalFunction 5.4.3
Residual 4.5.1
ResidualFunction 4.5.2
Residuum 4.5.1

## S

SaturatedFittingFormation 5.2.2
SaturatedFormation 4.4.2
Schunck class, attributes of 4.2
Schunck class, creating 4.1
Schunck class, operations for 4.2
Schunck classes and formations 4.0
SchunckClass 4.1.1
Set theoretical classes 2.0
set, of all primes 6.3.1
SetIsFittingClass 3.3.3
SetIsFittingFormation 3.3.12
SetIsFormation 3.3
SetIsOrdinaryFormation 3.3.6
SetIsSaturatedFittingFormation 3.3.15
SetIsSaturatedFormation 3.3.9
Socle 7.2.1
SocleComplement 4.3.2
SocleComponents 7.2.3
SolubleSocle 7.2.2
SolubleSocleComponents 7.2.4
SolvableSocle 7.2.2
SolvableSocleComponents 7.2.4
supersoluble groups, class of 6.1
SupersolubleGroups 6.1
SupersolubleProjector 6.2.2
SupersolvableGroups 6.1
SupersolvableProjector 6.2.2

## T

trivial groups, class of 6.1
TrivialGroups 6.1

## U

Union 2.3.3

## V

View, for classes 2.1.3

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