C intro.tex 1. Introduction
I 1.0. FORMAT package
C classes.tex 2. Set theoretical classes
S 2.1. Creating set theoretical classes
I 2.1. classes!creation of
F 2.1. IsClass
F 2.1. Class
F 2.1. Class
F 2.1. View!for classes
F 2.1. Print!for classes
F 2.1. Display!for classes
F 2.1. element test!for classes
I 2.1. in!for classes
I 2.1. membership test!for classes
F 2.1. equality!for classes
F 2.1. comparison!for classes
S 2.2. Properties of classes
I 2.2. classes!properties of
I 2.2. properties!of classes
F 2.2. IsEmpty!for classes
F 2.2. MemberFunction
S 2.3. Lattice operations for classes
I 2.3. lattice operations!for classes
F 2.3. Complement
F 2.3. Intersection!of classes
F 2.3. Intersection!of classes
I 2.3. INTERSECTION_LIMIT
F 2.3. Union
F 2.3. Difference
C grpclass.tex 3. Generic group classes
S 3.1. Creating group classes
I 3.1. group classes!creation of
F 3.1. GroupClass
F 3.1. GroupClass
F 3.1. GroupClass
F 3.1. GroupClass
F 3.1. Intersection!of group classes
F 3.1. Intersection!of group classes
S 3.2. Properties of group classes
I 3.2. closure properties!of group classes
I 3.2. group classes!closure properties of
F 3.2. IsGroupClass
F 3.2. ContainsTrivialGroup
F 3.2. IsSubgroupClosed
F 3.2. IsNormalSubgroupClosed
F 3.2. IsQuotientClosed
F 3.2. IsResiduallyClosed
F 3.2. IsNormalProductClosed
F 3.2. IsDirectProductClosed
F 3.2. IsSchunckClass
F 3.2. IsSaturated
S 3.3. Additional properties of group classes
I 3.3. group classes!properties of
I 3.3. properties!of group classes
F 3.3. HasIsFittingClass
F 3.3. IsFittingClass
F 3.3. SetIsFittingClass
F 3.3. HasIsOrdinaryFormation
I 3.3. HasIsFormation
F 3.3. IsOrdinaryFormation
I 3.3. IsFormation
F 3.3. SetIsOrdinaryFormation
I 3.3. SetIsFormation
F 3.3. HasIsSaturatedFormation
F 3.3. IsSaturatedFormation
F 3.3. SetIsSaturatedFormation
F 3.3. HasIsFittingFormation
F 3.3. IsFittingFormation
F 3.3. SetIsFittingFormation
F 3.3. HasIsSaturatedFittingFormation
F 3.3. IsSaturatedFittingFormation
F 3.3. SetIsSaturatedFittingFormation
S 3.4. Attributes of group classes
I 3.4. group classes!attributes for
I 3.4. attributes!of group classes
F 3.4. Characteristic
C schunck.tex 4. Schunck classes and formations
S 4.1. Creating Schunck classes
I 4.1. Schunck class!creating
F 4.1. SchunckClass
S 4.2. Attributes and operations for Schunck classes
I 4.2. Schunck class!attributes of
I 4.2. Schunck class!operations for
I 4.2. attributes!of Schunck class
I 4.2. operations!for Schunck class!
F 4.2. Boundary
F 4.2. Basis
F 4.2. Projector
F 4.2. CoveringSubgroup
F 4.2. BoundaryFunction
F 4.2. ProjectorFunction
S 4.3. Additional attributes for primitive soluble groups
I 4.3. primitive soluble group!attributes of
I 4.3. attributes!of primitive soluble group
F 4.3. IsPrimitiveSolubleGroup
F 4.3. IsPrimitiveSoluble
F 4.3. IsPrimitiveSolvableGroup
F 4.3. IsPrimitiveSolvable
F 4.3. SocleComplement
S 4.4. Creating formations
I 4.4. formations!creating
F 4.4. OrdinaryFormation
F 4.4. SaturatedFormation
F 4.4. FormationProduct
F 4.4. FittingFormationProduct
S 4.5. Attributes and operations for formations
I 4.5. formations!attributes for
I 4.5. formations!operations for
I 4.5. attributes!of formation
I 4.5. operations!for formation
F 4.5. Residual
F 4.5. Residuum
F 4.5. ResidualFunction
F 4.5. LocalDefinitionFunction
S 4.6. Low level functions for normal subgroups related to residuals
I 4.6. normal subgroups!with properties inherited by normal subgroups above
I 4.6. invariant normal subgroups!with properties inherited by normal subgroups above
I 4.6. normal subgroups!with properties inherited by factor groups
I 4.6. normal subgroups!with properties inherited by quotients
F 4.6. OneInvariantSubgroupMinWrtQProperty
F 4.6. AllInvariantSubgroupsWithQProperty
F 4.6. OneNormalSubgroupMinWrtQProperty
F 4.6. AllNormalSubgroupsWithQProperty
C fitting.tex 5. Fitting classes and Fitting sets
S 5.1. Creating Fitting classes
I 5.1. Fitting classes!creating
F 5.1. FittingClass
F 5.1. FittingProduct
I 5.1. FittingFormationProduct
S 5.2. Creating Fitting formations
I 5.2. Fitting formations!creating
I 5.2. formations!creating Fitting formations
I 5.2. Fitting classes!creating Fitting formations
F 5.2. FittingFormation
F 5.2. SaturatedFittingFormation
S 5.3. Creating Fitting sets
I 5.3. Fitting sets!creating
F 5.3. IsFittingSet
F 5.3. FittingSet
F 5.3. ImageFittingSet
F 5.3. PreImageFittingSet
F 5.3. Intersection!of Fitting sets
S 5.4. Attributes and operations for Fitting classes and Fitting sets
I 5.4. attributes!of Fitting sets
I 5.4. attributes!of Fitting classes
I 5.4. operations!for Fitting sets
I 5.4. operations!for Fitting classes
I 5.4. Fitting sets!operations for
I 5.4. Fitting classes!operations for
I 5.4. Fitting sets!attributes of
I 5.4. Fitting classes!attributes of
F 5.4. Radical
F 5.4. Injector
F 5.4. RadicalFunction
F 5.4. InjectorFunction
S 5.5. Low level functions for normal subgroups related to radicals
I 5.5. normal subgroups!with properties inherited by normal subgroups
I 5.5. invariant normal subgroups!with properties inherited by normal subgroups
F 5.5. OneInvariantSubgroupMaxWrtNProperty
F 5.5. AllInvariantSubgroupsWithNProperty
F 5.5. OneNormalSubgroupWithNProperty
F 5.5. AllNormalSubgroupsWithNProperty
C examples.tex 6. Examples of group classes
S 6.1. Pre-defined group classes
F 6.1. class!of all trivial groups
I 6.1. TrivialGroups
I 6.1. trivial groups!class of
I 6.1. class!of all trivial groups
F 6.1. class!of all nilpotent groups
I 6.1. NilpotentGroups
I 6.1. nilpotent groups!class of
I 6.1. class!of all nilpotent groups
F 6.1. class!of all supersoluble groups
F 6.1. class!of all supersoluble groups
I 6.1. SupersolubleGroups
I 6.1. SupersolvableGroups
I 6.1. supersoluble groups!class of
I 6.1. class!of all supersoluble groups
F 6.1. class!of all abelian groups
I 6.1. AbelianGroups
I 6.1. abelian groups!class of
I 6.1. class!of all abelian groups
F 6.1. AbelianGroupsOfExponent
I 6.1. AbelianGroupsOfExponent
I 6.1. class!of all abelian groups of bounded exponent
I 6.1. abelian groups of bounded exponent!class of
F 6.1. PiGroups
I 6.1. class!of all $\pi $-groups
F 6.1. PGroups
I 6.1. class!of all $p$-groups
S 6.2. Pre-defined projector functions
F 6.2. NilpotentProjector
I 6.2. Carter subgroup
F 6.2. SupersolubleProjector
F 6.2. SupersolvableProjector
S 6.3. Pre-defined sets of primes
F 6.3. set!of all primes
I 6.3. AllPrimes
I 6.3. primes!set of all
C normal.tex 7. Lists of normal subgroups
S 7.1. Functions for normal and characteristic subgroups
F 7.1. NormalSubgroups
F 7.1. CharacteristicSubgroups
F 7.1. MinimalNormalSubgroups
I 7.1. minimal normal subgroups
F 7.1. MinimalNormalPSubgroups
I 7.1. minimal normal $p$-subgroups
F 7.1. AbelianMinimalNormalSubgroups
I 7.1. minimal normal subgroups
S 7.2. Functions for the socle of finite groups
F 7.2. Socle
F 7.2. AbelianSocle
F 7.2. SolubleSocle
F 7.2. SolvableSocle
F 7.2. SocleComponents
F 7.2. AbelianSocleComponents
F 7.2. SolubleSocleComponents
F 7.2. SolvableSocleComponents
F 7.2. PSocle
F 7.2. PSocleComponents
F 7.2. PSocleSeries
