Analytic pro-p groups

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...

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Main Author: Dixon, John D.
Format: eBook
Language:English
Published: Cambridge Cambridge University Press 1999
Edition:Second edition
Series:Cambridge studies in advanced mathematics
Subjects:
Online Access:
Collection: Cambridge Books Online - Collection details see MPG.ReNa
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100 1 |a Dixon, John D. 
245 0 0 |a Analytic pro-p groups  |c J.D. Dixon [and three others] 
250 |a Second edition 
260 |a Cambridge  |b Cambridge University Press  |c 1999 
300 |a xviii, 368 pages  |b digital 
505 0 |a Pt. 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 -- Pt. 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 -- Pt. III. Further topics -- 10. Pro-p groups of finite coclass -- 11. Dimension subgroup methods -- 12. Some graded algebras -- Interlude D. The Golod-Shafarevich inequality -- Interlude E. Groups of sub-exponential growth -- 13. Analytic groups over pro-p rings -- App. A. The Hall-Petrescu formula -- App. B. Topological groups 
653 |a Nilpotent groups 
653 |a p-adic groups 
041 0 7 |a eng  |2 ISO 639-2 
989 |b CBO  |a Cambridge Books Online 
490 0 |a Cambridge studies in advanced mathematics 
856 |u https://doi.org/10.1017/CBO9780511470882  |x Verlag  |3 Volltext 
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520 |a 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