A Classification of the flag-transitive $2$-$(v,3,\lambda)$ designs with with $v\equiv 1,3\pmod{6}$ and $v \equiv 6 \pmod{\lambda}$

Abstract

In this paper, we provide a complete classification of the $2$-$(v,3,\lambda )$ designs with $v\equiv 1,3\pmod{6}$ and $% v \equiv 6 \pmod{\lambda}$ admitting a flag-transitive automorphism group non-isomorphic to a subgroup of $A\Gamma L_{1}(v)$.