# CRISP : a GAP 4 package - Index

A B C D E F G H I L M N O P Q 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
AbelianMinimalNormalSubgroups 5.5.7
AbelianSocle 5.5.2
AbelianSocleComponents 5.5.4
Additional attributes for primitive solvable groups 4.3
Additional properties of group classes 3.3
AllInvariantSubgroupsWithNProperty 5.6.2
AllInvariantSubgroupsWithQProperty 4.7.2
AllNormalSubgroupsWithNProperty 5.6.3
AllNormalSubgroupsWithQProperty 4.7.4
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 solvable 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 4.6.2
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 supersolvable groups 6.1.3 6.1
class, of all trivial groups 6.1.1 6.1
classes, creating 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
CRISP 1.0

## 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

factor groups, with properties inherited by factor groups 4.7
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 minimal normal subgroups and the socle 5.5
Functions for normal and characteristic subgroups 4.6

## G

Generic group classes 3.0
group classes, attributes for 3.4
group classes, closure properties of 3.2
group classes, creation 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 5.6
invariant normal subgroups, with properties inherited by normal subgroups above 4.7
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
IsPrimitiveSolvable 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
LocalDefinitionFunction 4.5.3
Low level functions for normal subgroups related to radicals 5.6
Low level functions for normal subgroups related to residuals 4.7

## M

MemberFunction 2.2.2
membership test, for classes 2.1
minimal normal subgroups 5.5

## N

nilpotent groups, class of 6.1
NilpotentProjector 6.2.1
normal subgroups, with properties inherited by normal subgroups 5.6
normal subgroups, with properties inherited by normal subgroups above 4.7
NormalSubgroups 4.6.1

## O

OneInvariantSubgroupMaxWrtNProperty 5.6.1
OneInvariantSubgroupMinWrtQProperty 4.7.1
OneNormalSubgroupMinWrtQProperty 4.7.3
OneNormalSubgroupWithNProperty 5.6.3
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 solvable 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 5.5.5
PSocleComponents 5.5.6

## Q

quotient groups, with properties inherited by quotients 4.7

## R

Radical 5.4.1
RadicalFunction 5.4.3
Residual 4.5.1
ResidualFunction 4.5.2

## 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 5.5.1
SocleComplement 4.3.2
SocleComponents 5.5.3
SolvableSocle 5.5.2
SolvableSocleComponents 5.5.4
supersolvable groups, class of 6.1
SupersolvableProjector 6.2.2

## T

trivial groups, class of 6.1

## U

Union 2.3.3

## V

View, for classes 2.1.3

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