We prove a Structure theorem for a class of finite transitive permutation groups that arises in the study of finite bipartite vertextransitive graphs. The class consists of all finite transitive permutation groups such that each non-trivial normal subgroup has at most two orbits, and at least one such subgroup is intransitive. The theorem is analogous to the O'Nan-Scott Theorem for finite primitive permutation groups, and this in turn is a refinement of the Baer Structure Theorem for finite primitive groups. An application is given for arc-transitive graphs.
|Journal||Illinois Journal of Mathematics|
|Publication status||Published - 2003|