An Erdős–Ko–Rado theorem for finite 2-transitive groups

We prove an analogue of the classical Erdős–Ko–Rado theorem for intersecting sets of permutations in finite 2-transitive groups. Given a finite group GG acting faithfully and 2-transitively on the set ΩΩ, we show that an intersecting set of maximal size in GG has cardinality |G|/|Ω||G|/|Ω|. This generalises and gives a unifying proof of some similar recent results in the literature.