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Analytic pro-p groups

Dixon, John D.

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Analytic pro-p groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	Analytic pro-p groups/ J.D. Dixon ... [et al.].
other author:	Dixon, John D.
Published:	Cambridge :Cambridge University Press, : 1999.,
Description:	xviii, 368 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	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.
Subject:	Nilpotent groups. -
Online resource:	https://doi.org/10.1017/CBO9780511470882
ISBN:	9780511470882

Analytic pro-p groups
Analytic pro-p groups[electronic resource] /J.D. Dixon ... [et al.]. - Second edition. - Cambridge :Cambridge University Press,1999. - xviii, 368 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;61. - Cambridge studies in advanced mathematics ;61..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

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.

ISBN: 9780511470882Subjects--Topical Terms:

704980
Nilpotent groups.

LC Class. No.: QA177

Dewey Class. No.: 512.2

Analytic pro-p groups
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020 $a 9780511470882 $q (electronic bk.)
020 $a 9780521650113 $q (hardback)
020 $a 9780521542180 $q (paperback)
035 $a CR9780511470882
040 $a UkCbUP $b eng $c UkCbUP $d GP
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245 0 0 $a Analytic pro-p groups $h [electronic resource] / $c J.D. Dixon ... [et al.].
250 $a Second edition.
260 $a Cambridge : $b Cambridge University Press, $c 1999.
300 $a xviii, 368 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 61
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.
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.
650 0 $a Nilpotent groups. $3 704980
650 0 $a p-adic groups. $3 560910
700 1 $a Dixon, John D. $3 518196
830 0 $a Cambridge studies in advanced mathematics ; $v 61. $3 3470414
856 4 0 $u https://doi.org/10.1017/CBO9780511470882