Analytic Pro-P Groups
Analytic Pro-P Groups
M. P. F. Du Sautoy, University of Cambridge
A. Mann, Hebrew University of Jerusalem
D. Segal, University of Oxford
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.
- Second edition of classic book
- Topic of much interest
- Authors well known
Product details
No date availablePaperback
9780521542180
388 pages
230 × 154 × 23 mm
0.6kg
60 exercises
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.
