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Analytic Pro-P Groups

Analytic Pro-P Groups

2nd Edition


Part of Cambridge Studies in Advanced Mathematics

  • Date Published: September 2003
  • availability: Available
  • format: Paperback
  • isbn: 9780521542180

£ 32.99

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About the Authors
  • 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.

    • Second edition of classic book
    • Topic of much interest
    • Authors well known
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    Product details

    • Edition: 2nd Edition
    • Date Published: September 2003
    • format: Paperback
    • isbn: 9780521542180
    • length: 388 pages
    • dimensions: 230 x 154 x 23 mm
    • weight: 0.6kg
    • contains: 60 exercises
    • availability: Available
  • Table of Contents

    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 Poincaré 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.

  • Authors

    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

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