Reduction for flag-transitive symmetric designs with k > λ(λ − 2)

Abstract

Let G be a flag-transitive automorphism group of a symmetric (v,k,λ) design D with k>λ(λ−2). O'Reilly Regueiro proved that if G is point-imprimitive, then D has parameters (v,k,λ)=(λ2(λ+2),λ(λ+1),λ). In the present paper, we consider the case that G is point-primitive. By applying the O'Nan-Scott Theorem, we prove that G must be of affine type or almost simple type.