Derangements in simple and primitive groups

Details Derangements in simple and primitive groups Derangements in simple and primitive groups

2002-08-03

arxiv.org/abs/math/0208022v1

Mathematics

Group Theory

To appear in Proceedings of Durham Conference on Groups, Geometry, and Combinatorics (2001)

Scientific paper

We investigate the proportion of fixed point free permutations (derangements) in finite transitive permutation groups. This article is the first in a series where we prove a conjecture of Shalev that the proportion of such elements is bounded away from zero for a simple finite group. In fact, there are much stronger results. This article focuses on finite Chevalley groups of bounded rank. We also discuss derangements in algebraic groups and in more general primitive groups. These results have applications in questions about probabilistic generation of finite simple groups and maps between varieties over finite fields.

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