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∈Pq such that pπ=pσ. 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 Pq. © 2010.
Meagher, K., Spiga, P. (2011). An Erdős-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective line. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 118(2), 532-544 [10.1016/j.jcta.2010.11.003].
An Erdős-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective line
SPIGA, PABLO
2011
Abstract
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∈Pq such that pπ=pσ. 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 Pq. © 2010.
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