The Erdős-Ko-Rado Property for Some 2-Transitive Groups.

A subset S of a group G ≤ Sym( n) is intersecting if for any pair of permutations $${\pi, \sigma \in S}$$ there is an $${i \in {1, 2, . . . , n}}$$ such that $${\pi (i) = \sigma (i)}$$ . It has been shown, using an algebraic approach, that the largest intersecting sets in each of Sym( n), Alt( n), and PGL(2, q) are exactly the cosets of the point-stabilizers. In this paper, we show how this approach can be applied more generally to many 2-transitive groups. We then apply this method to the Mathieu groups and to all 2-transitive groups with degree no more than 20. [ABSTRACT FROM AUTHOR]