Classical Groups, Derangements and Primes

A graduate-level introduction to finite classical groups featuring a comprehensive account of the conjugacy and geometry of elements of prime order.

Timothy C. Burness (Author), Michael Giudici (Author)

9781107629448, Cambridge University Press

Paperback / softback, published 15 January 2016

366 pages, 3 b/w illus. 60 tables
22.8 x 15 x 2.2 cm, 0.29 kg

'This book should be an indispensable reference for anybody doing research, or wanting to do research, in this area. Even for nonspecialists, however, chapters 2 and 3 should be a useful source of information on classical groups.' Mark Hunacek, The Mathematical Gazette

A classical theorem of Jordan states that every finite transitive permutation group contains a derangement. This existence result has interesting and unexpected applications in many areas of mathematics, including graph theory, number theory and topology. Various generalisations have been studied in more recent years, with a particular focus on the existence of derangements with special properties. Written for academic researchers and postgraduate students working in related areas of algebra, this introduction to the finite classical groups features a comprehensive account of the conjugacy and geometry of elements of prime order. The development is tailored towards the study of derangements in finite primitive classical groups; the basic problem is to determine when such a group G contains a derangement of prime order r, for each prime divisor r of the degree of G. This involves a detailed analysis of the conjugacy classes and subgroup structure of the finite classical groups.

Preface
Notational conventions
1. Introduction
2. Finite classical groups
3. Conjugacy classes
4. Subspace actions
5. Non-subspace actions
6. Low-dimensional classical groups
Appendix A. Number-theoretic miscellanea
Appendix B. Tables
References
Index.

Subject Areas: Topology [PBP], Number theory [PBH], Groups & group theory [PBG], Algebra [PBF], Mathematics [PB]