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New Horizons in pro-p Groups

  • Marcus du Sautoy
  • Dan Segal
  • Aner Shalev

Part of the Progress in Mathematics book series (PM, volume 184)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. C. R. Leedham-Green, S. McKay
    Pages 55-74
  3. Luis Ribes, Pavel Zalesskii
    Pages 75-119
  4. R. I. Grigorchuk
    Pages 121-179
  5. John S. Wilson
    Pages 181-203
  6. Rachel Camina
    Pages 205-221
  7. Avinoam Mann
    Pages 233-247
  8. Marcus du Sautoy, Dan Segal
    Pages 249-286
  9. Peter Symonds, Thomas Weigel
    Pages 349-410
  10. Back Matter
    Pages 411-426

About this book

Introduction

A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis­ covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.

Keywords

Finite Group theory Lie Topology algebra algebraic number theory finite and infinite group theory function number theory topology of Lie groups

Editors and affiliations

  • Marcus du Sautoy
    • 1
  • Dan Segal
    • 2
  • Aner Shalev
    • 3
  1. 1.Centre for Mathematical SciencesDPMMSCambridgeUK
  2. 2.All Souls CollegeOxfordUK
  3. 3.Institute of MathematicsHebrew UniversityJerusalemIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1380-2
  • Copyright Information Springer Science+Business Media New York 2000
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7122-2
  • Online ISBN 978-1-4612-1380-2
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site