Abstract
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.
• Provides an introduction to the basic properties and geometry of classical groups accessible to graduate students and researchers working in related areas • Gives the first unified account of conjugacy and geometry of elements in classical groups bringing together results previously scattered throughout the literature • Material on the study of derangements will be of particular interest to researchers working in the field of permutation groups
• Provides an introduction to the basic properties and geometry of classical groups accessible to graduate students and researchers working in related areas • Gives the first unified account of conjugacy and geometry of elements in classical groups bringing together results previously scattered throughout the literature • Material on the study of derangements will be of particular interest to researchers working in the field of permutation groups
Original language  English 

Publisher  Cambridge University Press 
Number of pages  366 
ISBN (Print)  9781107629448 
Publication status  Published  15 Jan 2016 
Publication series
Name  Australian Mathematical Society Lecture Series 

Volume  25 
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Professor Tim Burness
 School of Mathematics  Professor of Pure Mathematics
 Pure Mathematics
 Algebra
Person: Academic , Member