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A Course in the Theory of Groups

  • Textbook
  • © 1996

Overview

Authors:
  1. Derek J. S. Robinson

    1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

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

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Fundamental Concepts of Group Theory

    • Derek J. S. Robinson
    Pages 1-43

  3. Free Groups and Presentations

    • Derek J. S. Robinson
    Pages 44-62

  4. Decompositions of a Group

    • Derek J. S. Robinson
    Pages 63-92

  5. Abelian Groups

    • Derek J. S. Robinson
    Pages 93-120

  6. Soluble and Nilpotent Groups

    • Derek J. S. Robinson
    Pages 121-158

  7. Free Groups and Free Products

    • Derek J. S. Robinson
    Pages 159-191

  8. Finite Permutation Groups

    • Derek J. S. Robinson
    Pages 192-212

  9. Representations of Groups

    • Derek J. S. Robinson
    Pages 213-251

  10. Finite Soluble Groups

    • Derek J. S. Robinson
    Pages 252-284

  11. The Transfer and Its Applications

    • Derek J. S. Robinson
    Pages 285-309

  12. The Theory of Group Extensions

    • Derek J. S. Robinson
    Pages 310-355

  13. Generalizations of Nilpotent and Soluble Groups

    • Derek J. S. Robinson
    Pages 356-384

  14. Subnormal Subgroups

    • Derek J. S. Robinson
    Pages 385-415

  15. Finiteness Properties

    • Derek J. S. Robinson
    Pages 416-449

  16. Infinite Soluble Groups

    • Derek J. S. Robinson
    Pages 450-478

  17. Back Matter

    Pages 479-502
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Keywords

About this book

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.

Reviews

Second Edition

D.J.S. Robinson

A Course in the Theory of Groups

"This book is an excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The fifteen chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties . . . This book is highly recommended."—ACTA SCIENTIARUM MATHEMATICARUM

Authors and Affiliations

  • Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

    Derek J. S. Robinson

Bibliographic Information

  • Book Title: A Course in the Theory of Groups

  • Authors: Derek J. S. Robinson

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4419-8594-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1996

  • Hardcover ISBN: 978-0-387-94461-6Published: 26 October 1995

  • Softcover ISBN: 978-1-4612-6443-9Published: 08 September 2012

  • eBook ISBN: 978-1-4419-8594-1Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XVII, 502

  • Topics: Group Theory and Generalizations

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