C preface.tex 1. Preface
C intro.tex 2. Introduction to polycyclic presentations
C collect.tex 3. Collectors
S 3.1. Constructing a Collector
F 3.1. FromTheLeftCollector
F 3.1. SetRelativeOrder
F 3.1. SetRelativeOrderNC
F 3.1. SetPower
F 3.1. SetPowerNC
F 3.1. SetConjugate
F 3.1. SetConjugateNC
F 3.1. SetCommutator
F 3.1. UpdatePolycyclicCollector
F 3.1. IsConfluent
S 3.2. Accessing Parts of a Collector
F 3.2. RelativeOrders
F 3.2. GetPower
F 3.2. GetPowerNC
F 3.2. GetConjugate
F 3.2. GetConjugateNC
F 3.2. NumberOfGenerators
F 3.2. ObjByExponents
F 3.2. ExponentsByObj
S 3.3. Special Features
F 3.3. IsWeightedCollector
F 3.3. AddHallPolynomials
F 3.3. String
F 3.3. FTLCollectorPrintTo
F 3.3. FTLCollectorAppendTo
F 3.3. UseLibraryCollector
F 3.3. USE_LIBRARY_COLLECTOR
F 3.3. DEBUG_COMBINATORIAL_COLLECTOR
F 3.3. USE_COMBINATORIAL_COLLECTOR
C defins.tex 4. Pcp-groups - polycyclically presented groups
S 4.1. Pcp-elements -- elements of a pc-presented group
F 4.1. PcpElementByExponentsNC
F 4.1. PcpElementByExponents
F 4.1. PcpElementByGenExpListNC
F 4.1. PcpElementByGenExpList
F 4.1. IsPcpElement
F 4.1. IsPcpElementRep
S 4.2. Methods for pcp-elements
F 4.2. Collector
F 4.2. Exponents
F 4.2. GenExpList
F 4.2. NameTag
F 4.2. Depth
F 4.2. LeadingExponent
F 4.2. RelativeOrderPcp
F 4.2. RelativeIndex
F 4.2. FactorOrder
F 4.2. NormingExponent
F 4.2. NormedPcpElement
S 4.3. Pcp-groups - groups of pcp-elements
F 4.3. PcpGroupByCollector
F 4.3. PcpGroupByCollectorNC
F 4.3. Group
F 4.3. Subgroup
C basics.tex 5. Basic methods and functions for pcp-groups
S 5.1. Elementary methods for pcp-groups
F 5.1. equality!subgroups
F 5.1. Size
F 5.1. Random
F 5.1. Index
F 5.1. membership
F 5.1. Elements
F 5.1. ClosureGroup
F 5.1. NormalClosure
F 5.1. HirschLength
F 5.1. CommutatorSubgroup
F 5.1. PRump
F 5.1. SmallGeneratingSet
S 5.2. Elementary properties of pcp-groups
F 5.2. IsSubgroup
F 5.2. IsNormal
F 5.2. IsNilpotentGroup
F 5.2. IsAbelian
F 5.2. IsElementaryAbelian
F 5.2. IsFreeAbelian
S 5.3. Subgroups of pcp-groups
F 5.3. Igs
F 5.3. Igs
F 5.3. IgsParallel
F 5.3. Ngs
F 5.3. Ngs
F 5.3. Cgs
F 5.3. Cgs
F 5.3. CgsParallel
F 5.3. SubgroupByIgs
F 5.3. SubgroupByIgs
F 5.3. AddToIgs
F 5.3. AddToIgsParallel
F 5.3. AddIgsToIgs
S 5.4. Polycyclic presentation sequences for subfactors
F 5.4. Pcp
F 5.4. Pcp
F 5.4. Pcp
F 5.4. Pcp
F 5.4. GeneratorsOfPcp
F 5.4. pcp!as list
F 5.4. Length
F 5.4. RelativeOrdersOfPcp
F 5.4. DenominatorOfPcp
F 5.4. NumeratorOfPcp
F 5.4. GroupOfPcp
F 5.4. OneOfPcp
F 5.4. ExponentsByPcp
F 5.4. PcpGroupByPcp
S 5.5. Factor groups of pcp-groups
F 5.5. NaturalHomomorphism
F 5.5. factor group
F 5.5. FactorGroup
S 5.6. Homomorphisms for pcp-groups
F 5.6. GroupHomomorphismByImages
F 5.6. Kernel
F 5.6. Image
F 5.6. Image
F 5.6. Image
F 5.6. PreImage
F 5.6. PreImagesRepresentative
F 5.6. IsInjective
S 5.7. Changing the defining pc-presentation
F 5.7. RefinedPcpGroup
F 5.7. PcpGroupBySeries
F 5.7. PcpGroupBySeries
S 5.8. Printing a pc-presentation
F 5.8. PrintPcpPresentation
F 5.8. PrintPcpPresentation
F 5.8. PrintFullPresentation
F 5.8. PrintFullPresentation
S 5.9. Converting to and from a presentation
F 5.9. IsomorphismPcpGroup
F 5.9. IsomorphismPcGroup
C libraries.tex 6. Libraries and examples of pcp-groups
S 6.1. Libraries of various types of polycyclic groups
F 6.1. AbelianPcpGroup
F 6.1. DihedralPcpGroup
F 6.1. UnitriangularPcpGroup
F 6.1. SubgroupUnitriangularPcpGroup
F 6.1. InfiniteMetacyclicPcpGroup
F 6.1. HeisenbergPcpGroup
F 6.1. MaximalOrderByUnitsPcpGroup
F 6.1. BurdeGrunewaldPcpGroup
S 6.2. Some asorted example groups
F 6.2. ExampleOfMetabelianPcpGroup
F 6.2. ExamplesOfSomePcpGroups
C methods.tex 7. Higher level methods for pcp-groups
S 7.1. Subgroup series in pcp-groups
F 7.1. PcpSeries
F 7.1. EfaSeries
F 7.1. SemiSimpleEfaSeries
F 7.1. DerivedSeries
F 7.1. RefinedDerivedSeries
F 7.1. RefinedDerivedSeriesDown
F 7.1. LowerCentralSeries
F 7.1. UpperCentralSeries
F 7.1. TorsionByPolyEFSeries
F 7.1. PcpsBySeries
F 7.1. PcpsBySeries
F 7.1. PcpsOfEfaSeries
S 7.2. Orbit stabilizer methods for pcp-groups
F 7.2. PcpOrbitStabilizer
F 7.2. PcpOrbitsStabilizers
F 7.2. StabilizerIntegralAction
F 7.2. OrbitIntegralAction
F 7.2. NormalizerIntegralAction
F 7.2. ConjugacyIntegralAction
S 7.3. Centralizers, Normalizers and Intersections
F 7.3. Centralizer!element in subgroup
F 7.3. IsConjugate!elements
F 7.3. Centralizer!subgroup in subgroup
F 7.3. Normalizer
F 7.3. IsConjugate!subgroups
F 7.3. Intersection
S 7.4. Finite subgroups
F 7.4. TorsionSubgroup
F 7.4. NormalTorsionSubgroup
F 7.4. IsTorsionFree
F 7.4. FiniteSubgroupClasses
F 7.4. FiniteSubgroupClassesBySeries
S 7.5. Subgroups of finite index and maximal subgroups
F 7.5. MaximalSubgroupClassesByIndex
F 7.5. LowIndexSubgroupClasses
F 7.5. LowIndexNormals
F 7.5. NilpotentByAbelianNormalSubgroup
S 7.6. Further attributes for pcp-groups based on the Fitting subgroup
F 7.6. FittingSubgroup
F 7.6. IsNilpotentByFinite
F 7.6. Centre
F 7.6. FCCentre
F 7.6. PolyZNormalSubgroup
F 7.6. NilpotentByAbelianByFiniteSeries
S 7.7. Functions for nilpotent groups
F 7.7. MinimalGeneratingSet
S 7.8. Random methods for pcp-groups
F 7.8. RandomOrbitStabilizerPcpGroup
F 7.8. RandomCentralizerPcpGroup
F 7.8. RandomCentralizerPcpGroup
F 7.8. RandomNormalizerPcpGroup
C cohom.tex 8. Cohomology for pcp-groups
S 8.1. Cohomology records
F 8.1. CRRecordByMats
F 8.1. CRRecordBySubgroup
F 8.1. CRRecordByPcp
S 8.2. Cohomology groups
F 8.2. OneCoboundariesCR
F 8.2. OneCocyclesCR
F 8.2. TwoCoboundariesCR
F 8.2. TwoCocyclesCR
F 8.2. OneCohomologyCR
F 8.2. TwoCohomologyCR
S 8.3. Extended 1-cohomology
F 8.3. OneCoboundariesEX
F 8.3. OneCocyclesEX
F 8.3. OneCohomologyEX
S 8.4. Extensions and Complements
F 8.4. ComplementCR
F 8.4. ComplementsCR
F 8.4. ComplementClassesCR
F 8.4. ComplementClassesEfaPcps
F 8.4. ComplementClasses
F 8.4. ExtensionCR
F 8.4. ExtensionsCR
F 8.4. ExtensionClassesCR
F 8.4. SplitExtensionPcpGroup
S 8.5. Constructing pcp groups as extensions
C matreps.tex 9. Matrix Representations
F 9.0. UnitriangularMatrixRepresentation
F 9.0. IsMatrixRepresentation
