Block-Transitive Automorphism Groups of $2$-$(v,5,\lambda )$ Designs

Chuhan Lei, Xiaoqin Zhan

This paper investigates $2$-$(v,5,\lambda )$ designs $\mathcal{D}$ admitting a block-transitive automorphism group $G$. We first prove that if $G$ is point-imprimitive, then $v$ must be o…