The Primitive Soluble Permutation Groups of Degree less than 256

  • Authors
  • Mark W. Short

Part of the Lecture Notes in Mathematics book series (LNM, volume 1519)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Mark W. Short
    Pages 1-9
  3. Mark W. Short
    Pages 10-42
  4. Mark W. Short
    Pages 108-113
  5. Mark W. Short
    Pages 114-120
  6. Mark W. Short
    Pages 146-146
  7. Back Matter
    Pages 121-145

About this book

Introduction

This monograph addresses the problem of describing all primitive soluble permutation groups of a given degree, with particular reference to those degrees less than 256. The theory is presented in detail and in a new way using modern terminology. A description is obtained for the primitive soluble permutation groups of prime-squared degree and a partial description obtained for prime-cubed degree. These descriptions are easily converted to algorithms for enumerating appropriate representatives of the groups. The descriptions for degrees 34 (die vier hochgestellt, Sonderzeichen) and 26 (die sechs hochgestellt, Sonderzeichen) are obtained partly by theory and partly by machine, using the software system Cayley. The material is appropriate for people interested in soluble groups who also have some familiarity with the basic techniques of representation theory. This work complements the substantial work already done on insoluble primitive permutation groups.

Keywords

Finite Groups Group Theory Permutation Prime Representation theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0090195
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55501-8
  • Online ISBN 978-3-540-47120-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book