Conjugacy classes of derangements in finite transitive groups

Resumo

Let G be a permutation group acting transitively on a finite set Ω. We classify all such (G, Ω) when G contains a single conjugacy class of derangements. This was done under the assumption that G acts primitively by Burness and Tong-Viet. It turns out that there are no imprimitive examples. We also discuss some results on the proportion of conjugacy classes which consist of derangements.