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.

We present some results on flag-transitive symmetric designs. First we see what conditions are necessary for a symmetric design to admit an imprimitive, flag-transitive automorphism group. Then we move on to study the possibilities for a primitive, flag-transitive automorphism group, and prove that for λ ≤ 3, the group must be affine or almost simple, and finally we analyse the case in which a ...

Among the properties of homogeneity of incidence structures flagtransitivity obviously is a particularly important and natural one. Consequently, in the last decades flag-transitive Steiner t-designs (i.e. flag-transitive t-(v, k, 1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been possible in recent years to essentially char...

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.

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).

This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every subgroup G automorphism group a nontrivial design primitive affine or almost simple type. Moreover, we classify designs admitting flag transitive with socle PSL(n,q) for some n≥3. Alongside this analysis give construction 2-(v,k−1,k−2) given 2-(...

A Steiner quadruple system of order v is a 3 − (v, 4, 1) design, and will be denoted SQS(v). Using the classification of finite 2-transitive permutation groups all SQS(v) with a flag-transitive automorphism group are completely classified, thus solving the ”still open and longstanding problem of classifying all flag-transitive 3− (v, k,1) designs” (cf. [5, p. 273], [6]) for the smallest value o...