An erdös-ko-rado theorem for the derangement graph of PGL3(q) acting on the projective plane

In this paper we prove an Erdös-Ko-Rado-type theorem for intersecting sets of permutations. We show that an intersecting set of maximal size in the projective general linear group PGL3(q), in its natural action on the points of the projective line, is either a coset of the stabilizer of a point or a coset of the stabilizer of a line. This gives the first evidence for the veracity of Conjecture 2 from K. Meagher and P. Spiga, An Erdös-Ko-Rado Theorem for the Derangement Graph of PGL(2, q) Acting on the Projective Line [J. Combin. Theory Ser. A, 118 (2011), pp. 532-544]. © 2014 Society for Industrial and Applied Mathematics.