Analytic pro-p groups
著者
書誌事項
Analytic pro-p groups
（Cambridge studies in advanced mathematics, 61）
Cambridge University Press, 1999
2nd ed., rev. and enl. / by Marcus du Sautoy & Dan Segal
- : hbk
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注記
Includes bibliographical references (p. 362-365) and index
内容説明・目次
内容説明
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.
目次
- 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.
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