Group and Ring Theoretic Properties of Polycyclic Groups

  • B.A.F. Wehrfritz
Part of the Algebra and Applications book series (AA, volume 10)

Table of contents

  1. Front Matter
    Pages I-VII
  2. B. A. F. Wehrfritz
    Pages 1-11
  3. B. A. F. Wehrfritz
    Pages 13-28
  4. B. A. F. Wehrfritz
    Pages 29-39
  5. B. A. F. Wehrfritz
    Pages 41-54
  6. B. A. F. Wehrfritz
    Pages 63-74
  7. B. A. F. Wehrfritz
    Pages 89-98
  8. B. A. F. Wehrfritz
    Pages 99-107
  9. B. A. F. Wehrfritz
    Pages 109-116
  10. Back Matter
    Pages 117-128

About this book

Introduction

Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations.

The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups.

Keywords

Group theory Noetherian rings Vector space algebra polycyclic groups ring theory

Authors and affiliations

  • B.A.F. Wehrfritz
    • 1
  1. 1.University of LondonQueen MaryLondonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84882-941-1
  • Copyright Information Springer-Verlag London 2009
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-84882-940-4
  • Online ISBN 978-1-84882-941-1