A Course in the Theory of Groups

  • Derek J. S. Robinson

Part of the Graduate Texts in Mathematics book series (GTM, volume 80)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Derek J. S. Robinson
    Pages 1-43
  3. Derek J. S. Robinson
    Pages 44-62
  4. Derek J. S. Robinson
    Pages 63-92
  5. Derek J. S. Robinson
    Pages 93-120
  6. Derek J. S. Robinson
    Pages 121-158
  7. Derek J. S. Robinson
    Pages 159-191
  8. Derek J. S. Robinson
    Pages 192-212
  9. Derek J. S. Robinson
    Pages 213-251
  10. Derek J. S. Robinson
    Pages 252-284
  11. Derek J. S. Robinson
    Pages 285-309
  12. Derek J. S. Robinson
    Pages 310-355
  13. Derek J. S. Robinson
    Pages 356-384
  14. Derek J. S. Robinson
    Pages 385-415
  15. Derek J. S. Robinson
    Pages 416-449
  16. Derek J. S. Robinson
    Pages 450-478
  17. Back Matter
    Pages 479-502

About this book

Introduction

A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra.
This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included. There are three main additions to the book. In the chapter on group extensions an exposition of Schreier's concrete approach via factor sets is given before the introduction of covering groups. This seems to be desirable on pedagogical grounds. Then S. Thomas's elegant proof of the automorphism tower theorem is included in the section on complete groups. Finally an elementary counterexample to the Burnside problem due to N.D. Gupta has been added in the chapter on finiteness properties.

Keywords

Abelian group Group theory algebra automorphism homological algebra ring theory

Authors and affiliations

  • Derek J. S. Robinson
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-8594-1
  • Copyright Information Springer Science+Business Media New York 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6443-9
  • Online ISBN 978-1-4419-8594-1
  • Series Print ISSN 0072-5285
  • About this book