Derangements in simple and primitive groups

By Jason E. Fulman, Robert M. Guralnick. 2002

51 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/31f8b11c6af4f8bb97da0ad05c2949cb231c4c8d

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In Artificial Intelligence

In Discrete Mathematics and Combinatorics

In Electrical and Electronic Engineering

Citations in the corpus

On fixed points of permutations (2007, background): “However, the analog of the previous theorem is proved in [36] if the rank of the Chevalley group is fixed.”