The Erdos-Ko-Rado (EKR) theorem is a classical result in extremal set
theory. It states that when k < n=2, any family of k-subsets of an n-set
X, with the property that any two subsets in the family have nonempty
intersection, has size at most
; equality holds if and only if the family
consists of all k-subsets of X containing a xed point.
Here we consider EKR type problems for permutation groups. In par-
ticular, we focus on the action of the 2-dimensional projective special linear
group PSL(2; q) on the projective line PG(1; q) over the nite eld Fq, where
q is an odd prime power. A subset S of PSL(2; q) is said to be an inter-
secting family if for any g1; g2 2 S, there exists an element x 2 PG(1; q)
such that xg1 = xg2 . It is known that the maximum size of an intersecting
family in PSL(2; q) is q(q ?? 1)=2. We prove that all intersecting families of
maximum size are cosets of point stabilizers for all odd prime powers q > 3.