Infinite Linear Groups

An Account of the Group-theoretic Properties of Infinite Groups of Matrices

  • Bertram A. F. Wehrfritz
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 76)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Bertram A. F. Wehrfritz
    Pages 1-16
  3. Bertram A. F. Wehrfritz
    Pages 17-40
  4. Bertram A. F. Wehrfritz
    Pages 41-49
  5. Bertram A. F. Wehrfritz
    Pages 50-71
  6. Bertram A. F. Wehrfritz
    Pages 72-81
  7. Bertram A. F. Wehrfritz
    Pages 82-89
  8. Bertram A. F. Wehrfritz
    Pages 90-100
  9. Bertram A. F. Wehrfritz
    Pages 101-111
  10. Bertram A. F. Wehrfritz
    Pages 112-133
  11. Bertram A. F. Wehrfritz
    Pages 134-154
  12. Bertram A. F. Wehrfritz
    Pages 155-173
  13. Bertram A. F. Wehrfritz
    Pages 174-185
  14. Bertram A. F. Wehrfritz
    Pages 186-201
  15. Bertram A. F. Wehrfritz
    Pages 202-218
  16. Back Matter
    Pages 219-232

About this book

Introduction

By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor­ phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.

Keywords

Abelian group Finite Group theory Groups Groups of Matrices Morphism Unendliche lineare Gruppe

Authors and affiliations

  • Bertram A. F. Wehrfritz
    • 1
  1. 1.Queen Mary CollegeLondon UniversityLondonEngland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-87081-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1973
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-87083-5
  • Online ISBN 978-3-642-87081-1
  • Series Print ISSN 0071-1136
  • About this book