Handbook of Computational Group Theory

Handbook of Computational Group Theory

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The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics.The Handbook of Computational Group Theory offers the first complete treatment of all the fundamental methods and algorithms in CGT presented at a level accessible even to advanced undergraduate students. It develops the theory of algorithms in full detail and highlights the connections between the different aspects of CGT and other areas of computer algebra. While acknowledging the importance of the complexity analysis of CGT algorithms, the authors' primary focus is on algorithms that perform well in practice rather than on those with the best theoretical complexity.Throughout the book, applications of all the key topics and algorithms to areas both within and outside of mathematics demonstrate how CGT fits into the wider world of mathematics and science. The authors include detailed pseudocode for all of the fundamental algorithms, and provide detailed worked examples that bring the theorems and algorithms to life.show more

Product details

  • Hardback | 536 pages
  • 160 x 236 x 32mm | 1,401.61g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 24 Tables, black and white; 6 Illustrations, black and white
  • 1584883723
  • 9781584883722
  • 1,922,843

Table of contents

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 AlgorithmsApplicationsshow more

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