New horizons in pro-p groups

Author(s)

• Du Sautoy, Marcus
• Segal, Daniel, Ph. D.
• Shalev, Aner

Bibliographic Information

New horizons in pro-p groups

Marcus du Sautoy, Dan Segal, Aner Shalev, editors

（Progress in mathematics, v. 184）

Birkhäuser, c2000

• : us
• : sz

Note

Includes bibliographical references and index

Description and Table of Contents

Volume

: us ISBN 9780817641719

Description

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.

Table of Contents

1. Lie Methods in the Theory of pro-p Groups.- 2. On the Classification of p-groups and pro-p Groups.- 3. Pro-p Trees and Applications.- 4. Just Infinite Branch Groups.- 5. On Just Infinite Abstract and Profinite Groups.- 6. The Nottingham Group.- 7. On Groups Satisfying the Golod-Shafarevich Condition.- 8. Subgroup Growth in pro-p Groups.- 9. Zeta Functions of Groups.- 10. Where the Wild Things are: Ramification Groups and the Nottingham Group.- 11. p-adic Galois Representations and pro-p Galois Groups.- 12. Cohomology of p-adic Analytic Groups.- Appendix: Further Problems.

Volume

: sz ISBN 9783764341718

Description

Beyond the established theory of p-adic analytic groups, the theory of pro-p groups has seen important advances. These include the construction of new classes of groups and new applications in number theory. This text presents accounts of these and other topics.

Table of Contents

• Lie methods in the theory of pro-p groups, A. Shalev
• on the classification of prop-p groups and finite p-groups, C.R. Leedham-Green, S. McKay
• prop-p trees and applications, L. Ribes, P. Zalesskii
• just infinite branch groups, R. I. Grigorchuk
• on just infinite abstract and profinite groups, J.S. Wilson
• the Nottingham group, R. Camina
• on groups satisfying the Golod-Shafarevich condition, E. Zelmanov
• sub-group growth in prop-p groups, A. Mann
• zeta functions of groups, M. du Sautoy, D. Segal
• where the wild things are - ramification groups and the Nottingham group, M. du Sautoy, I. Fesenko
• p-adic Galois representations and prop-p Galois groups, N. Boston
• the cohomology of p-adic analytic groups, P. Symonds, T. Weigel. Appendix: further problems.

by "Nielsen BookData"

Details

• NCID: BA47341348
• ISBN:
  • 0817641718
  • 3764341718
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boston
• Pages/Volumes: xiii, 423 p.
• Size: 24 cm
• Classification:
  • LCC : QA177.N48
• Subject Headings:
  • LCSH : Nilpotent groups
  • LCSH : p-adic groups
• Parent Bibliography ID:
  • BA00018010