An Erdos-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective plane

Abstract

Let G = PGL(2, q) be the projective general linear group acting on the projec- tive line P_q. A subset S of G is intersecting if for any pair of permutations \pi and \sigma in S, there is a projective point p in P_q such that \pi(p)= \sigma(p). We prove that if S is intersecting, then |S| <= q(q-1). Also, we prove that the only sets S that meet this bound are the cosets of the stabilizer of a point of P_q. Keywords: derangement graph, independent sets, Erdos-Ko-Rado