Analytic Pro-P Groups

J. D. Dixon; M. P. F. Du Sautoy; A. Mann; D. Segal

doi:10.1017/CBO9780511470882

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Analytic Pro-P Groups

Analytic Pro-P Groups

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Mann, Avionam 2000. An inequality for group presentations. Bulletin of the Australian Mathematical Society, Vol. 62, Issue. 3, p. 467.

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Symonds, Peter and Weigel, Thomas 2000. New Horizons in pro-p Groups. Vol. 184, Issue. , p. 349.

CrossRef

Google Scholar

du Sautoy, Marcus and Fesenko, Ivan 2000. New Horizons in pro-p Groups. Vol. 184, Issue. , p. 287.

CrossRef

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Camina, Rachel 2000. New Horizons in pro-p Groups. p. 205.

CrossRef

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du Sautoy, Marcus and Segal, Dan 2000. New Horizons in pro-p Groups. p. 249.

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Google Scholar

Kochloukova, Dessislava H. 2000. Metabelian pro-p groups of type FPm. Journal of Group Theory, Vol. 3, Issue. 4,

CrossRef

Google Scholar

Shalev, Aner 2000. New Horizons in pro-p Groups. p. 1.

CrossRef

Google Scholar

Ribes, Luis and Zalesskii, Pavel 2000. New Horizons in pro-p Groups. p. 75.

CrossRef

Google Scholar

Mann, Avinoam 2000. New Horizons in pro-p Groups. p. 233.

CrossRef

Google Scholar

Grigorchuk, R. I. 2000. New Horizons in pro-p Groups. p. 121.

CrossRef

Google Scholar

Sautoy, Marcus du 2000. The zeta function of sl2(ℤ). Forum Mathematicum, Vol. 12, Issue. 2,

CrossRef

Google Scholar

Boston, Nigel 2000. New Horizons in pro-p Groups. Vol. 184, Issue. , p. 329.

CrossRef

Google Scholar

Abdollahi, Alireza and Traustason, Gunnar 2002. On locally finite 𝑝-groups satisfying an Engel condition. Proceedings of the American Mathematical Society, Vol. 130, Issue. 10, p. 2827.

CrossRef

Google Scholar

Ochi, Yoshihiro and Venjakob, Otmar 2002. On the structure of Selmer groups over 𝑝-adic Lie extensions. Journal of Algebraic Geometry, Vol. 11, Issue. 3, p. 547.

CrossRef

Google Scholar

Jaikin-Zapirain, A. 2002. Finite groups of bounded rank with an almost regular automorphism. Israel Journal of Mathematics, Vol. 129, Issue. 1, p. 209.

CrossRef

Google Scholar

Morishita, M. 2002. On certain analogies between knots and primes. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2002, Issue. 550,

CrossRef

Google Scholar

Jaikin-Zapirain, A. and Moretó, Alexander 2002. Character degrees and nilpotence class of finite 𝑝-groups: An approach via pro-𝑝 groups. Transactions of the American Mathematical Society, Vol. 354, Issue. 10, p. 3907.

CrossRef

Google Scholar

Jaikin-Zapirain, Andrei and Piontkovski, Dmitri 2003. On the Growth of Noetherian Filtered Rings. Communications in Algebra, Vol. 31, Issue. 1, p. 505.

CrossRef

Google Scholar

ABÉRT, MIKLÓS LUBOTZKY, ALEXANDER and PYBER, LÁSZLÓ 2003. BOUNDED GENERATION AND LINEAR GROUPS. International Journal of Algebra and Computation, Vol. 13, Issue. 04, p. 401.

CrossRef

Google Scholar

Wilson, Lawrence E. 2003. Dimension subgroups andp-th powers inp-groups. Israel Journal of Mathematics, Vol. 138, Issue. 1, p. 1.

CrossRef

Google Scholar

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2nd edition
J. D. Dixon, Carleton University, Ottawa, M. P. F. Du Sautoy, University of Cambridge, A. Mann, Hebrew University of Jerusalem, D. Segal, University of Oxford

Publisher:: Cambridge University Press
Online publication date:: December 2009
Print publication year:: 1999
Online ISBN:: 9780511470882
DOI:: https://doi.org/10.1017/CBO9780511470882

Subjects:: Mathematics (general), Mathematics, Algebra
Series:: Cambridge Studies in Advanced Mathematics (61)

61.99 (GBP)

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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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Analytic Pro-P Groups

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-ix

Introduction
pp x-xv

Notation
pp xvi-xviii

Prelude A reminder
pp 1-12

Part I - Pro-p groups
pp 13-14

1 - Profinite groups and pro-p groups
pp 15-36

2 - Powerful p-groups
pp 37-47

3 - Pro-p groups of finite rank
pp 48-60

4 - Uniformly powerful groups
pp 61-86

5 - Automorphism groups
pp 87-96

Interlude A - ‘Fascicule de résultats’: pro-p groups of finite rank
pp 97-98

Part II - Analytic groups
pp 99-100

6 - Normed algebras
pp 101-137

7 - The group algebra
pp 138-170

Interlude B - Linearity criteria
pp 171-177

8 - p-adic analytic groups
pp 178-205

Interlude C - Finitely generated groups, p-adic analytic groups and Poincaré series
pp 206-212

9 - Lie theory
pp 213-240

Part III - Further topics
pp 241-242

10 - Pro-p groups of finite coclass
pp 243-269

11 - Dimension subgroup methods
pp 270-290

12 - Some graded algebras
pp 291-310

Interlude D - The Golod–Shafarevich inequality
pp 311-318

Interlude E - Groups of sub-exponential growth
pp 319-321

13 - Analytic groups over pro-p rings
pp 322-354

Appendix A - The Hall–Petrescu formula
pp 355-357

Appendix B - Topological groups
pp 358-361

Bibliography
pp 362-365

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