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

Abstract

In this paper, we provide a complete classification of the $2$-$(v,3,\lambda )$ designs with $v\equiv 1,3(\mathrm{mod}6)$ and admitting a flag-transitive automorphism group non-isomorphic to a subgroup of $A\Gamma L_1(v)$.