Overview

This 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 Details

Author:   Gregory Butler
Publisher:   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:  

9783540549550

ISBN 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  
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Table of Contents

Group 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.

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