Analytic Pro-P Groups

An up-to-date treatment of analytic pro-p groups for graduate students and researchers.

J. D. Dixon (Author), M. P. F. Du Sautoy (Author), A. Mann (Author), D. Segal (Author)

9780521542180, Cambridge University Press

Paperback, published 18 September 2003

388 pages, 60 exercises
23 x 15.4 x 2.3 cm, 0.6 kg

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.

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.

Subject Areas: Groups & group theory [PBG]