Flag-transitive point-primitive 2-(v,k,4) symmetric designs and two dimensional classical groups

Let D be a 2-（v, k, 4） symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ≥G ≤Aut（X） where X ≌ PSL2（q）.Then D is a 2-（15,8,4） symmetric design with X = PSL2（9） and Xx = PGL2（3） where x is a point of D.

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.

Exceptional groups of Lie type and flag-transitive triplanes

A triplane is a ( v, k, 3)-symmetric design. Let G be a subgroup of the full automorphism group of a triplane D. In this paper we prove that if G is flag-transitive and point-primitive, then the socle of G cannot be a simple exceptional group of Lie type.

Sporadic groups and flag-transitive triplanes

Let D be a triplane, i.e., a 2-(v,k,3) symmetric design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G is flag-transitive point-primitive, then the socle of G cannot be a sporadic simple group.

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.