書誌事項

Analytic pro-p groups

J.D. Dixon ... [et al.]

(Cambridge studies in advanced mathematics, 61)

Cambridge University Press, 2003

2nd ed., rev. and enl. / by Marcus du Sautoy & Dan Segal

  • : pbk

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注記

Other authors: M.P.F. du Sautoy, A. Mann, D. Segal

"First published 1991. Second edition 1999. First paperback edition 2003"--T.p. verso

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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詳細情報

  • NII書誌ID(NCID)
    BB05410521
  • ISBN
    • 9780521542180
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    xviii, 368 p.
  • 大きさ
    23 cm
  • 分類
  • 件名
  • 親書誌ID
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