Unsolvable block transitive automorphism groups of 2-(v,k,1)(k=6,7,8,9) designs

AbstractIn this paper, we study block transitive automorphism groups of 2-(v,k,1) block designs. Let D be a 2-(v,k,1)(k=6,7,8,9) design admitting a block transitive, point primitive but not flag transitive group G of automorphisms. We prove that if G is unsolvable, then G does not admit an exceptional simple group of Lie type as its socle. Moreover, for a 2-(v,9,1) design, we also prove that there does not exist any block transitive, point imprimitive, unsolvable group G of automorphisms