Analytic Pro-P Groups
2nd Edition
Part of Cambridge Studies in Advanced Mathematics
- Authors:
- 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
- Date Published: September 2003
- availability: Available
- format: Paperback
- isbn: 9780521542180
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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.
Read more- Second edition of classic book
- Topic of much interest
- Authors well known
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×Product details
- Edition: 2nd Edition
- Date Published: September 2003
- format: Paperback
- isbn: 9780521542180
- length: 388 pages
- dimensions: 230 x 154 x 23 mm
- weight: 0.6kg
- contains: 60 exercises
- availability: Available
Table of Contents
Prelude
Part I. Pro-p Groups:
1. Profinite groups and pro-p groups
2. Powerful p-groups
3. Pro-p groups of finite rank
4. Uniformly powerful groups
5. Automorphism groups
Interlude A. Fascicule de resultats: pro-p groups of finite rank
Part II. Analytic Groups:
6. Normed algebras
7. The group algebra
Interlude B. Linearity criteria
8. P-adic analytic groups
Interlude C. Finitely generated groups, p-adic analytic groups and Poincaré series
9. Lie theory
Part III. Further Topics:
10. Pro-p groups of finite co-class
11. Dimension subgroup methods
12. Some graded algebras
Interlude D. The Golod Shafarevic inequality
Interlude E. Groups of sub-exponential growth
13. Analytic groups over pro-p rings.
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