Analytic Pro-P Groups (Cambridge Studies in Advanced Mathematics No.61 2nd Revised edition)

Analytic Pro-P Groups (Cambridge Studies in Advanced Mathematics No.61 2nd Revised edition)

By: John D. Dixon (author), A. Mann (author), D. Segal (author), M.P.F.Du Sautoy (author), A. Katok (series_editor), W. Fulton (series_editor), B. Bollobas (series_editor), Simon Simon (series_editor), F. Kirwan (series_editor), Sarnak Sarnak (series_editor)Paperback

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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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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 Poincare 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.

Product Details

  • publication date: 18/09/2003
  • ISBN13: 9780521542180
  • Format: Paperback
  • Number Of Pages: 388
  • ID: 9780521542180
  • weight: 570
  • ISBN10: 0521542189
  • edition: 2nd Revised edition

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