Cambridge University Press eBooks· 2015· Book chapter
Classical Groups, Derangements and Primes
- 96citations
- 2015year
Short summary
This book introduces finite classical groups by detailing the conjugacy and geometry of elements of prime order, specifically tailored for studying derangements in primitive classical groups.
AI-generated from the title and abstract; the full text is not read.
Key points
- Focuses on the conjugacy and geometry of elements of prime order in finite classical groups.
- Aims to determine when a primitive classical group G contains a derangement of prime order r for each prime divisor r of its degree.
- Requires detailed analysis of conjugacy classes and subgroup structure of these groups.
- Builds upon Jordan's theorem regarding derangements in finite transitive permutation groups.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2015 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics