  A subset of a group G of Sym(n) is intersecting if for any pair of
permutations $\pi,\sigma \in G$ 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 method can
be applied more generally to many 2-transitive groups. We then apply this
method to the Mathieu groups and to all 2-transtive groups with degree no more
than 20.
