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Table of contents

  1. Front Matter
  2. Pages 1-6
  3. Pages 14-23
  4. Pages 44-55
  5. Pages 64-70
  6. Pages 71-77
  7. Pages 78-97
  8. Pages 98-116
  9. Pages 117-128
  10. Pages 129-142
  11. Pages 156-170
  12. Pages 171-183
  13. Pages 229-232
  14. Back Matter

About this book

Introduction

This is the first-ever book on computational group theory. It provides extensive and up-to-date coverage of the fundamental algorithms for permutation groups with reference to aspects of combinatorial group theory, soluble groups, and p-groups where appropriate. The book begins with a constructive introduction to group theory and algorithms for computing with small groups, followed by a gradual discussion of the basic ideas of Sims for computing with very large permutation groups, and concludes with algorithms that use group homomorphisms, as in the computation of Sylowsubgroups. No background in group theory is assumed. The emphasis is on the details of the data structures and implementation which makes the algorithms effective when applied to realistic problems. The algorithms are developed hand-in-hand with the theoretical and practical justification.All algorithms are clearly described, examples are given, exercises reinforce understanding, and detailed bibliographical remarks explain the history and context of the work. Much of the later material on homomorphisms, Sylow subgroups, and soluble permutation groups is new.

Keywords

Algebraic Algorithms Algebraische Algorithmen Computational Complexity Computational Group Theory Graph Graph Algorithms Graph-Algorithmen Group theory Komplexität und Algorithmen Permutatioen und Kombinationen Permutations and Combinations algorithms data structures

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-54955-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54955-0
  • Online ISBN 978-3-540-46607-9
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349
  • Buy this book on publisher's site