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

摘要

Let G = PGL(2, q) be the projective general linear group acting on the projective line Pq. A subset S of G is intersecting if for any pair of permutations π,σ in S, there is a projective point p ∈ P_q such that p~π = p~σ. 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.