Transactions of the American Mathematical Society· 2012Q1
Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements
- 141citations
- Q1SCImago
- 2012year
Short summary
New explicit upper bounds are established for the number and sizes of conjugacy classes in finite Chevalley groups, with applications to derangements in simple groups.
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Key points
- Presents explicit upper bounds for the number and sizes of conjugacy classes in finite Chevalley groups.
- These bounds have prior applications in zeta functions, random walks, and the Ore conjecture.
- Solves a strong version of the Boston-Shalev conjecture on derangements for most primitive permutation group representations of simple groups.
AI-generated from the title and abstract; the full text is not read.
Abstract
We present explicit upper bounds for the number and size of conjugacy classes in finite Chevalley groups and their variations. These results have been used by many authors to study zeta functions associated to representations of finite simple groups, random walks on Chevalley groups, the final solution to the Ore conjecture about commutators in finite simple groups and other similar problems. In this paper, we solve a strong version of the Boston-Shalev conjecture on derangements in simple groups for most of the families of primitive permutation group representations of finite simple groups (the remaining cases are settled in two other papers of the authors and applications are given in a third).
The authors' abstract, as published at the source. Transactions of the American Mathematical Society, 2012 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics