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Permutation Groups

  • John D. Dixon
  • Brian Mortimer

Part of the Graduate Texts in Mathematics book series (GTM, volume 163)

Table of contents

  1. Front Matter
    Pages i-xii
  2. John D. Dixon, Brian Mortimer
    Pages 1-32
  3. John D. Dixon, Brian Mortimer
    Pages 33-64
  4. John D. Dixon, Brian Mortimer
    Pages 65-105
  5. John D. Dixon, Brian Mortimer
    Pages 106-142
  6. John D. Dixon, Brian Mortimer
    Pages 143-176
  7. John D. Dixon, Brian Mortimer
    Pages 177-209
  8. John D. Dixon, Brian Mortimer
    Pages 210-254
  9. John D. Dixon, Brian Mortimer
    Pages 255-273
  10. John D. Dixon, Brian Mortimer
    Pages 274-301
  11. Back Matter
    Pages 302-348

About this book

Introduction

Permutation Groups form one of the oldest parts of group theory. Through the ubiquity of group actions and the concrete representations which they afford, both finite and infinite permutation groups arise in many parts of mathematics and continue to be a lively topic of research in their own right. The book begins with the basic ideas, standard constructions and important examples in the theory of permutation groups.It then develops the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal O'Nan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. This text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, or for self- study. It includes many exercises and detailed references to the current literature.

Keywords

Algebraic structure Group theory algebra automorphism classification graphs group action

Authors and affiliations

  • John D. Dixon
    • 1
  • Brian Mortimer
    • 1
  1. 1.Department of Mathematics and StatisticsCarleton UniversityOttawaCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0731-3
  • Copyright Information Springer-Verlag New York, Inc. 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6885-7
  • Online ISBN 978-1-4612-0731-3
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site