‎Let $G$ be a finite group‎. ‎The degree pattern of $G$ denoted by‎ ‎$D(G)$ is defined as follows‎: ‎If $pi(G)={p_{1},p_{2},...,p_{k}}$ such that‎ ‎$p_{1}

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).

Abstract We present a new method for showing that groups are virtually special. This is done by considering finite quotients and linear characters. use this to show an infinite family of groups, related Bestvina-Brady branching, provides examples special outside hyperbolic context.

‎let $g$ be a finite group‎. ‎the degree pattern of $g$ denoted by‎ ‎$d(g)$ is defined as follows‎: ‎if $pi(g)={p_{1},p_{2},...,p_{k}}$ such that‎ ‎$p_{1}

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).

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