Unsolvable block transitive automorphism groups of 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. heorem lock transitive group of automorphisms of a 2 - ( v , 5 , 1 ) design is unsolvable, then it is flag transitive.