Lectures on Profinite Topics in Group Theory
£53.99
Part of London Mathematical Society Student Texts
- Authors:
- Benjamin Klopsch, Royal Holloway, University of London
- Nikolay Nikolov, Imperial College London
- Christopher Voll, Universität Bielefeld, Germany
- Editor: Dan Segal, All Souls College, Oxford
- Date Published: February 2011
- availability: Available
- format: Paperback
- isbn: 9780521183017
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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.
Read more- 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
Preface
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
Index.
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