Flag-transitive automorphism groups of $2$-designs with $\hat{I}»\ge (r,\hat{I}»{)}^2$ are not product type

Abstract

In this paper we show that a flag-transitive automorphism group $G$ of a non-trivial $2$-$(v,k,\hat{I}»)$ design with $\hat{I}»\ge (r,\hat{I}»{)}^2$ is not of product action type. In conclusion, $G$ is a primitive group of affine or almost simple type.

13 pages,2 figures