An Erdős-Ko-Rado theorem for finite \(2\)-transitive groups

Abstract

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 (G) acting faithfully and (2)-transitively on the set (\Omega), we show that an intersecting set of maximal size in (G) has cardinality (|G|/|\Omega|). This generalises and gives a unifying proof of some similar recent results in the literature.