Steiner triple systems with doubly transitive automorphism groups: A corollary to the classification theorem for finite simple groups

Abstract

Assuming that the classification theorem for finite simple groups is complete, a conjecture of M. Hall ( Proc. Sympos. Pure Math. 6 (1962) , 47–66; and in “Proceedings of the International Conference on Theory of Groups”, pp. 115–144, Australian National University, Canberra, Australia, 1965) that a Steiner triple system with a doubly transitive automorphism group is a projective or affine geometry, is verified.