Lectures on Profinite Topics in Group Theory
Published on 10. February 2011
Book
Paperback/Softback
158 pages
978-0-521-18301-7 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 9 mm
Weight
240 gr
ISBN-13
978-0-521-18301-7 (9780521183017)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Benjamin Klopsch | Nikolay Nikolov | Christopher Voll
Lectures on Profinite Topics in Group Theory
E-Book
12/2011
1st Edition
Cambridge University Press
€53.49
Available for download
Benjamin Klopsch | Nikolay Nikolov | Christopher Voll
Lectures on Profinite Topics in Group Theory
Book
02/2011
Cambridge University Press
€135.16
Article not available at the moment
Persons
Benjamin Klopsch is a Senior Lecturer in the Department of Mathematics at Royal Holloway, University of London. Nikolay Nikolov is a Reader in Mathematics in the Department of Mathematics at Imperial College London. Christopher Voll is a Lecturer in the School of Mathematics at the University of Southampton. Dan Segal is a Senior Research Fellow at All Souls College, Oxford.
Content
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.