Analytic Pro-P Groups

J. D. Dixon; M. P. F. Du Sautoy; A. Mann; D. Segal

doi:10.1017/CBO9780511470882

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2nd edition
J. D. Dixon, Carleton University, Ottawa, M. P. F. Du Sautoy, University of Cambridge, A. Mann, Hebrew University of Jerusalem, D. Segal, University of Oxford

Publisher:: Cambridge University Press
Online publication date:: December 2009
Print publication year:: 1999
Online ISBN:: 9780511470882
DOI:: https://doi.org/10.1017/CBO9780511470882

Subjects:: Mathematics (general), Mathematics, Algebra
Series:: Cambridge Studies in Advanced Mathematics (61)

61.99 (GBP)

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The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank, starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I, it is possible to define these, and derive all the main results of p-adic Lie theory, without having to develop any sophisticated analytic machinery. Part III, consisting of new material, takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass, the dimension subgroup series, and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers.

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Analytic Pro-P Groups

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-ix

Introduction
pp x-xv

Notation
pp xvi-xviii

Prelude A reminder
pp 1-12

Part I - Pro-p groups
pp 13-14

1 - Profinite groups and pro-p groups
pp 15-36

2 - Powerful p-groups
pp 37-47

3 - Pro-p groups of finite rank
pp 48-60

4 - Uniformly powerful groups
pp 61-86

5 - Automorphism groups
pp 87-96

Interlude A - ‘Fascicule de résultats’: pro-p groups of finite rank
pp 97-98

Part II - Analytic groups
pp 99-100

6 - Normed algebras
pp 101-137

7 - The group algebra
pp 138-170

Interlude B - Linearity criteria
pp 171-177

8 - p-adic analytic groups
pp 178-205

Interlude C - Finitely generated groups, p-adic analytic groups and Poincaré series
pp 206-212

9 - Lie theory
pp 213-240

Part III - Further topics
pp 241-242

10 - Pro-p groups of finite coclass
pp 243-269

11 - Dimension subgroup methods
pp 270-290

12 - Some graded algebras
pp 291-310

Interlude D - The Golod–Shafarevich inequality
pp 311-318

Interlude E - Groups of sub-exponential growth
pp 319-321

13 - Analytic groups over pro-p rings
pp 322-354

Appendix A - The Hall–Petrescu formula
pp 355-357

Appendix B - Topological groups
pp 358-361

Bibliography
pp 362-365

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