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Finiteness Conditions and Generalized Soluble Groups

Part 1

  • Book
  • © 1972

Overview

Authors:
  1. Derek J. S. Robinson

    1. University of Illinois, Urbana, USA

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 62)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XV
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  2. Fundamental Concepts in the Theory of Infinite Groups

    • Derek J. S. Robinson
    Pages 1-41

  3. Soluble and Nilpotent Groups

    • Derek J. S. Robinson
    Pages 42-64

  4. Maximal and Minimal Conditions

    • Derek J. S. Robinson
    Pages 65-100

  5. Finiteness Conditions on Conjugates and Commutators

    • Derek J. S. Robinson
    Pages 101-142

  6. Finiteness Conditions on the Normal and Subnormal Structure of a Group

    • Derek J. S. Robinson
    Pages 143-186

  7. Back Matter

    Pages 187-212
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Keywords

About this book

This book is a study of group theoretical properties of two dis­ parate kinds, firstly finiteness conditions or generalizations of fini­ teness and secondly generalizations of solubility or nilpotence. It will be particularly interesting to discuss groups which possess properties of both types. The origins of the subject may be traced back to the nineteen twenties and thirties and are associated with the names of R. Baer, S. N. Cernikov, K. A. Hirsch, A. G. Kuros, 0.]. Schmidt and H. Wie­ landt. Since this early period, the body of theory has expanded at an increasingly rapid rate through the efforts of many group theorists, particularly in Germany, Great Britain and the Soviet Union. Some of the highest points attained can, perhaps, be found in the work of P. Hall and A. I. Mal'cev on infinite soluble groups. Kuras's well-known book "The theory of groups" has exercised a strong influence on the development of the theory of infinite groups: this is particularly true of the second edition in its English translation of 1955. To cope with the enormous increase in knowledge since that date, a third volume, containing a survey of the contents of a very large number of papers but without proofs, was added to the book in 1967.

Authors and Affiliations

  • University of Illinois, Urbana, USA

    Derek J. S. Robinson

Bibliographic Information

  • Book Title: Finiteness Conditions and Generalized Soluble Groups

  • Book Subtitle: Part 1

  • Authors: Derek J. S. Robinson

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-662-07241-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1972

  • Hardcover ISBN: 978-3-540-05620-1Published: 05 September 1972

  • Softcover ISBN: 978-3-642-05713-7Published: 19 October 2010

  • eBook ISBN: 978-3-662-07241-7Published: 14 March 2013

  • Edition Number: 1

  • Number of Pages: XVI, 212

  • Topics: Group Theory and Generalizations

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