let $g$ be an automorphism group of a‎ ‎$2$-$(v,k,4)$ symmetric design $mathcal d$‎. ‎in this paper‎, ‎we‎ ‎prove that if $g$ is flag-transitive point-primitive‎, ‎then the‎ ‎socle of $g$ cannot be an exceptional group of lie type‎.

Let $R$ be a ring with identity and $I(X,R)$ the incidence of locally finite partially ordered set $X$ over $R.$ In this paper, we compute socle singular ideal for some in terms $R$, respectively.

 After the classification of the flag-transitive linear spaces, the attention has been turned to line-transitive linear spaces. In this article, we present a partial classification of the finite linear spaces $mathcal S$ on which an almost simple group $G$ with the socle $G_2(q)$ acts line-transitively.