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Lectures on Profinite Topics in Group Theory


Part of London Mathematical Society Student Texts

  • Date Published: February 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521183017

£ 47.99

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About the Authors
  • In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.

    • Exercises, some with solutions, provide a deeper understanding of the subject
    • Numerous examples give the reader hands-on experience
    • Suitable for self-study or seminar series and contains a guide to more advanced literature
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    Product details

    • Date Published: February 2011
    • format: Paperback
    • isbn: 9780521183017
    • length: 158 pages
    • dimensions: 228 x 152 x 10 mm
    • weight: 0.24kg
    • contains: 50 exercises
    • availability: Available
  • Table of Contents

    Editor's introduction
    Part I. An Introduction to Compact p-adic Lie Groups:
    1. Introduction
    2. From finite p-groups to compact p-adic Lie groups
    3. Basic notions and facts from point-set topology
    4. First series of exercises
    5. Powerful groups, profinite groups and pro-p groups
    6. Second series of exercises
    7. Uniformly powerful pro-p groups and Zp-Lie lattices
    8. The group GLd(Zp), just-infinite pro-p groups and the Lie correspondence for saturable pro-p groups
    9. Third series of exercises
    10. Representations of compact p-adic Lie groups
    References for Part I
    Part II. Strong Approximation Methods:
    11. Introduction
    12. Algebraic groups
    13. Arithmetic groups and the congruence topology
    14. The strong approximation theorem
    15. Lubotzky's alternative
    16. Applications of Lubotzky's alternative
    17. The Nori–Weisfeiler theorem
    18. Exercises
    References for Part II
    Part III. A Newcomer's Guide to Zeta Functions of Groups and Rings:
    19. Introduction
    20. Local and global zeta functions of groups and rings
    21. Variations on a theme
    22. Open problems and conjectures
    23. Exercises
    References for Part III

  • Authors

    Benjamin Klopsch, Royal Holloway, University of London
    Benjamin Klopsch is a Senior Lecturer in the Department of Mathematics at Royal Holloway, University of London.

    Nikolay Nikolov, Imperial College London
    Nikolay Nikolov is a Reader in Mathematics in the Department of Mathematics at Imperial College London.

    Christopher Voll, Universität Bielefeld, Germany
    Christopher Voll is a Lecturer in the School of Mathematics at the University of Southampton.


    Dan Segal, All Souls College, Oxford
    Dan Segal is a Senior Research Fellow at All Souls College, Oxford.

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