Intersecting families of permutations

Let Sn be the symmetric group on the set X={1,2,…,n}. A subset S of Sn is intersecting if for any two permutations g and h in S, g(x)=h(x) for some x∈X (that is g and h agree on x). Deza and Frankl (J. Combin. Theory Ser. A 22 (1977) 352) proved that if S⊆Sn is intersecting then |S|≤(n−1)!. This bound is met by taking S to be a coset of a stabiliser of a point. We show that these are the only largest intersecting sets of permutations.