Derangements in simple and primitive groups
群论
2007-05-23 v1 组合数学
摘要
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.
引用
@article{arxiv.math/0208022,
title = {Derangements in simple and primitive groups},
author = {Jason Fulman and Robert Guralnick},
journal= {arXiv preprint arXiv:math/0208022},
year = {2007}
}
备注
To appear in Proceedings of Durham Conference on Groups, Geometry, and Combinatorics (2001)