Handbook of Computational Group Theory (Hardcover)

History of Computational Group Theory BACKGROUND MATERIALSFundamentalsGroup ActionsSeriesPresentation of GroupsPresentation of SubgroupsAbelian Group PresentationsRepresentation Theory, Modules, Extension, Derivations, and ComplementsField TheoryREPRESENTING GROUPS ON A COMPUTERRepresenting Groups on ComputersThe Use of Random Methods in CGTSome Structural CalculatorsComputing with HomorphismsCOMPUTATION IN FINITE PERMUTATION GROUPSThe Calculation of Orbits and StabilizersTesting for Alt (W) and Sym (W)Finding Block SystemsBases and Strong Generating SetsHomomorphisms from Permutation GroupsBacktrack SearchesSylow Subgroups, P-cores, and the Solvable RadicalApplicationsCOSET ENUMERATIONThe Basic ProcedureStrategies for Coset EnumerationPresentations of SubgroupsFinding All SubgroupsFinding All Subgroups Up to a Given IndexApplicationsPRESENTATION OF GIVEN GROUPSFinding a Presentation of a Given GroupFinding a Presentation of a Strong Generating SetThe Sims 'Verify' AlgorithmREPRESENTATIONS, COHOMOLOGY, AND CHARACTERSComputation in Finite FieldsElemetary Computational Linear AlgebraFactorizing Polynomials Over Finite FieldsTesting KG-Models for Irreducibility - The MeataxeRelated ComputationsCohomologyComputing Character TablesStructural Investigation of Matrix GroupsCOMPUTATION WITH POLYCYCLIC GROUPSPolycyclic PresentationsExamples of Polycyclic GroupsSubgroups and Membership TestingFactor Groups and HomomorphismsSubgroup SeriesOrbit-Stabilizer MethodsComplements and ExtensionsIntersections, Centralizers, and NormalizersAutomorphism GroupsThe Structure of Finite Solvable GroupsCOMPUTING QUOTIENTS OF FINITELY PRESENTED GROUPSFinite Quotients and Automorphism Groups of Finite GroupsAbelian QuotientsPractical Computation of the HNF and SNFP-Quotients of Finitely-Presented GroupsADVANCED COMPUTATIONS IN FINITE GROUPSSome Useful SubgroupsComputing Composition and Chief SeriesApplications of the Solvable Radical MethodComputing the Subgroups of a Finite GroupAppication - Enumerating Finite Unlabelled StructuresLIBRARIES AND DATABASESPrimitive Permutation GroupsTransitive Permutation GroupsPerfect GroupsThe Small Groups LibraryCrystallorgraphic GroupsOther DatabasesREWRITING SYSTEMSMonoid SystemsRewriting SystemsRewriting Systems in Monoids and GroupsRewriting Systems for Polycyclic GroupsVerifying NilpotencyApplicationsFINITE STATE AUTOMATA AND AUTOMATIC GROUPSFinite State AutomataAutomatic GroupsThe Algorithm to Compute Shortlex Automatic StructuresRelated AlgorithmsApplications