On a reduction theorem for finite, bipartite 2-arc-transitive graphs

Let r be a finite connecied regular bipartite 2-arc transitive graph. It is shown that r is a cover of a possibly smaller graph :E, which is also connecied and regular of the same valency as r, and there is a subgroup G of Aut :E such that G is 2-arc transitive on :E and every nontrivial normal subgroup of G has at most two orbits on vertices. Such graphs :E for which the subgroup G has an abelian normal subgroup with two orbits are investigated. It is shown that :E is a 2-arc transitive Cayley graph for either (a) an elementary abelian 2-group, or (b) a group < N, T >, where N is an elementary abelian group of odd order and T, an element of order 2, inverts every element of N. The graphs :E arising in (a) have been classified recently by A.A. Ivanov and the author.