(SIAM J. Discrete Math. 28, 2014) Meagher, Karen; Spiga, Pablo
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 \(PGL_3(q)\),
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 to the veracity
of Conjecture~\(2\) from K.~Meagher, P.~Spiga, An Erdős-Ko-Rado theorem for
the derangement graph of \(\mathrm{PGL}(2,q)\) acting on the
projective line, \( \textit{J. Comb. Theory Series A} \textbf{118} \)
(2011), 532--544.
