SUZUKI GROUPS Sz(q) AND 2-(v,k,1) BLOCK DESIGNS

It is proved that if D be a 2|(v,k,1) design with G≤ Aut D block primitive then G does not have a Suzuki group Sz(q) as the socle.

2-(v,k,1) DESIGNS AND PSL (3,q) WHERE q IS ODD

Let G be a block-primitive automorphism group of a 2-(v,k,1) design.If G is isomorphic to PSL (3,q) where q is odd,then G is also point-primitive.

Steinberg triality groups acting on 2-(v,k,1)designs

A 2 - (v, k, 1) design D = (P,B) is a system consisting of a finite set P of v points and a collection B of k-subsets of P, called blocks, such that each 2-subset of P is contained in precisely one block.Let G be an automorphism group of a 2 - (v, k, 1) design. Delandtsheer proved that if G is block-primitive and D is not a projective plane, then G is almost simple, that is, T ≤ G ≤ Aut(T), where T is a non-abelian simple group. In this paper, we prove that T is not isomorphic to 3D4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design.

Block-Transitive 2-(v,k,1) Designs and Groups E_6(q)

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, pointprimitive but not flag-transitive automorphism group G. 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 simple group E6（q） as its socle.