Abstract:

Let ${\cal S}$=$({\cal P},{\cal B})$

be a nontrivial $3$-$(v,7,\lambda)$ design with $\lambda\geq 2$. In this paper we show that if $G$ is a block-transitive automorphism group of $\cal S$, then $G$ is point-primitive of affine

or almost simple type. In addition, the case that $G$ is a finite almost simple group with an alternating group socle $A_n$ is considered as well.

Key words: Automorphism group, Block-transitive, 3-design