On Primitive Representations of Finite Alternating and Symmetric Groups with a 2-Transitive Subconstituent Original Research Article

In this paper we analyse primitive permutation representations of finite alternating and symmetric groups which have a 2-transitive subconstituent. We show that either the representation belongs to an explicit list of known examples, or the point stabiliser is a known almost-simple 2-transitive group and acts primitively in the natural representation of the associated alternating or symmetric group.