25 Finite Polycyclic Groups
Ag groups (see Words in Finite Polycyclic Groups) are a subcategory of
finitely generated groups (see Groups).
The following sections describe how subgroups of ag groups are
represented (see More about Ag Groups), additional operators and record
Ag Group Functions and Subgroups and Properties of Ag Groups). Some additional
information about generating systems of subgroups and factor groups are
Factor Groups of Ag Groups.
One Cohomology Group describes how to compute the groups of one
coboundaries and one cocycles for given ag groups. Complements gives
informations how to obtain complements and conjugacy classes of
complements for given ag groups.
Subsections
- More about Ag Groups
- Construction of Ag Groups
- Ag Group Operations
- Ag Group Records
- Set Functions for Ag Groups
- Elements for Ag Groups
- Intersection for Ag Groups
- Size for Ag Groups
- Group Functions for Ag Groups
- AsGroup for Ag Groups
- Group for Ag Groups
- CommutatorSubgroup for Ag Groups
- Normalizer for Ag Groups
- IsCyclic for Ag Groups
- IsNormal for Ag Groups
- IsSubgroup for Ag Groups
- Stabilizer for Ag Groups
- CyclicGroup for Ag Groups
- ElementaryAbelianGroup for Ag Groups
- DirectProduct for Ag Groups
- WreathProduct for Ag Groups
- RightCoset for Ag Groups
- FpGroup for Ag Groups
- Ag Group Functions
- AgGroup
- IsAgGroup
- AgGroupFpGroup
- IsConsistent
- IsElementaryAbelianAgSeries
- MatGroupAgGroup
- PermGroupAgGroup
- RefinedAgSeries
- ChangeCollector
- The Prime Quotient Algorithm
- PQuotient
- Save
- PQp
- InitPQp
- FirstClassPQp
- NextClassPQp
- Weight
- Factorization for PQp
- The Solvable Quotient Algorithm
- SolvableQuotient
- InitSQ
- ModulesSQ
- NextModuleSQ
- Generating Systems of Ag Groups
- AgSubgroup
- Cgs
- Igs
- IsNormalized
- Normalize
- Normalized
- MergedCgs
- MergedIgs
- Factor Groups of Ag Groups
- FactorGroup for AgGroups
- CollectorlessFactorGroup
- FactorArg
- Subgroups and Properties of Ag Groups
- CompositionSubgroup
- HallSubgroup
- PRump
- RefinedSubnormalSeries
- SylowComplements
- SylowSystem
- SystemNormalizer
- MinimalGeneratingSet
- IsElementAgSeries
- IsPNilpotent
- NumberConjugacyClasses
- Exponents
- FactorsAgGroup
- MaximalElement
- Orbitalgorithms of Ag Groups
- AffineOperation
- AgOrbitStabilizer
- LinearOperation
- Intersections of Ag Groups
- ExtendedIntersectionSumAgGroup
- IntersectionSumAgGroup
- SumAgGroup
- SumFactorizationFunctionAgGroup
- One Cohomology Group
- OneCoboundaries
- OneCocycles
- Complements
- Complement
- Complementclasses
- CoprimeComplement
- ComplementConjugatingAgWord
- HallConjugatingWordAgGroup
- Example, normal closure
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GAP 3.4.4
April 1997