Block transitive automorphism groups of 2-(nu, k, 1) block designs

A 2-(u, k, 1) block design is a set Q of v points and a collection of k-subsets of 9, called blocks, such that any two points lie in a unique block. Such designs have been classified in [ l&S] if their automorphism group acts doubly transitively or doubly homogeneously on its points. A classification for the case of flag transitive automorphism groups is now under way Cl, 2, 91. In this paper we consider block transitive automorphism groups and take the first steps towards a classification in this situation. The paper can be seen as a continuation of the work in CL 151. The second section describes the notation and contains a number of preliminary results some of which may be folk lore. The third section contains the main results, in particular the following