The Erdős-Ko-Rado theorem for the derangement graph of the projective general linear group acting on the projective space

Abstract

In this paper we prove an Erdős-Ko-Rado-type theorem for intersecting sets of permutations. We show that an intersecting set of maximal size in the projective general linear group PGLn+1(q), in its natural action on the points of the n-dimensional projective space, is either a coset of the stabiliser of a point or a coset of the stabiliser of a hyperplane. This gives a positive solution to [15, Conjecture 2].