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170324 ||| eng |
| 020 |
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|a 9780511470882
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| 050 |
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4 |
|a QA177
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| 100 |
1 |
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|a Dixon, John D.
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| 245 |
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|a Analytic pro-p groups
|c J.D. Dixon [and three others]
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| 250 |
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|a Second edition
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| 260 |
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|a Cambridge
|b Cambridge University Press
|c 1999
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| 300 |
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|a xviii, 368 pages
|b digital
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| 505 |
0 |
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|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
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| 653 |
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|a Nilpotent groups
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| 653 |
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|a p-adic groups
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b CBO
|a Cambridge Books Online
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| 490 |
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|a Cambridge studies in advanced mathematics
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| 856 |
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|u https://doi.org/10.1017/CBO9780511470882
|x Verlag
|3 Volltext
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|a 512.2
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| 520 |
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|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
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