Block-transitive 2-[formula omitted] designs and the twisted simple groups [formula omitted].

This article is a contribution to the study of block-transitive automorphism groups of 2-(v, k, 1) block designs. Let D be a 2-(v, k, 1) design admitting a block-transitive, point-primitive but not flag-transitive group G of automorphisms. Let kr=(k, v-1) and q=pf for prime p. In this paper we prove that if G and D are as above and q>(3(krk-kr+1)f)1/3 then G does not admit a twisted simple group 2 E6(q) as its socle. [ABSTRACT FROM AUTHOR]