Lectures on profinite topics in group theory
著者
書誌事項
Lectures on profinite topics in group theory
（London Mathematical Society student texts, 77）
Cambridge University Press, 2011
- : hardback
- : pbk
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注記
Basically a record of lectures held Sept. 2007 in Oxford, organised by Dan Segal, sponsored by the London Mathematical Society and the EPSRC. Cf. pref
Includes bibliographical references and index
収録内容
- An introduction to compact p-adic Lie groups / by Benjamin Klopsch
- Strong approximation methods / by Nikolay Nikolov
- A newcomer's guide to zeta functions of groups and rings / by Christopher Voll
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780521183017
内容説明
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.
目次
- 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.
- 巻冊次
-
: hardback ISBN 9781107005297
内容説明
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.
目次
- 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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