Unsolvable block transitive automorphism groups of 2-(v,5,1) designs

This article is a contribution to the study of the automorphism groups of 2-(v,k,1) block designs. In particular we look at the unsolvable block transitive automorphism groups of 2-(v,5,1) designs and prove the following theorem.Main Theorem – If a block transitive group of automorphisms of a design is unsolvable, then it is flag transitive.