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OverviewThis is the first-ever book on computational group theory. It provides extensive and up-to-date coverage of thefundamental algorithms for permutation groups with referenceto aspects of combinatorial group theory, soluble groups,and p-groups where appropriate. The book begins with a constructive introduction to grouptheory and algorithms for computing with small groups,followed by a gradual discussion of the basic ideas of Simsfor computing with very large permutation groups, andconcludes with algorithms that use group homomorphisms, asin the computation of Sylowsubgroups. No background ingroup theory is assumed. The emphasis is on the details of the data structures andimplementation which makes the algorithms effective whenapplied to realistic problems. The algorithms are developedhand-in-hand with the theoretical and practicaljustification. All algorithms are clearly described,examples are given, exercises reinforce understanding, anddetailed bibliographical remarks explain the history andcontext of the work. Much of the later material on homomorphisms, Sylowsubgroups, and soluble permutation groups is new. Full Product DetailsAuthor: Gregory ButlerPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 1991 ed. Volume: 559 Dimensions: Width: 15.50cm , Height: 1.30cm , Length: 23.50cm Weight: 0.800kg ISBN: 9783540549550ISBN 10: 3540549552 Pages: 244 Publication Date: 27 November 1991 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsGroup theory background.- List of elements.- Searching small groups.- Cayley graph and defining relations.- Lattice of subgroups.- Orbits and schreier vectors.- Regularity.- Primitivity.- Inductive foundation.- Backtrack search.- Base change.- Schreier-Sims method.- Complexity of the Schreier-Sims method.- Homomorphisms.- Sylow subgroups.- P-groups and soluble groups.- Soluble permutation groups.- Some other algorithms.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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