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 - (υ, k, 1) design D = (?,?, ?) is a system consisting of a finite set ? of υ points and a collection ? of ?-subsets of ?, called blocks, such that each 2-subset of ? is contained in precisely one block. Let G be an automorphism group of a 2-(υ, 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 3 D 4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design.