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. RelativeOrder 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. PrintPcpPresentation F 5.8. PrintPcpPresentation 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 S 7.9. Non-abelian tensor product and Schur extensions F 7.9. SchurExtension F 7.9. SchurExtensionEpimorphism F 7.9. SchurCovering F 7.9. SchurMultiplicator F 7.9. NonAbelianExteriorSquareEpimorphism F 7.9. NonAbelianExteriorSquare F 7.9. NonAbelianTensorSquareEpimorphism F 7.9. NonAbelianExteriorSquarePlusEmbedding F 7.9. NonAbelianExteriorSquarePlusEmbedding F 7.9. NonAbelianTensorSquarePlusEpimorphism F 7.9. NonAbelianTensorSquarePlus F 7.9. WhiteheadQuadraticFunctor S 7.10. Schur covers and Schur towers F 7.10. SchurCovers 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 F 8.2. TwoCohomologyModCR 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 S 9.1. Unitriangular matrix groups F 9.1. UnitriangularMatrixRepresentation F 9.1. IsMatrixRepresentation S 9.2. Upper unitriangular matrix groups F 9.2. IsomorphismUpperUnitriMatGroupPcpGroup F 9.2. SiftUpperUnitriMatGroup F 9.2. RanksLevels F 9.2. MakeNewLevel F 9.2. SiftUpperUnitriMat F 9.2. DecomposeUpperUnitriMat