The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).

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.

Let R be a standard graded algebra over field k and I homogeneous ideal of R. We study the question whether there is constant c such that Soc(Hmj(R/It))<−ct=0 for all t≥1 variation this question. also draw connection between notion gauge-boundedness in prime characteristic.