Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements

By Jason E. Fulman, Robert M. Guralnick. 2009

145 citations recorded by the source corpus.

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).

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/efc862ab3213c7b8937287250bbbbd3586e66434

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In Artificial Intelligence

In Discrete Mathematics and Combinatorics

In Mathematical Physics

Citations in the corpus

Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras (2012, background): “In fact, there is an easy proof of the finiteness of outer unipotent classes given the finiteness of inner unipotent classes [1].”