Flag-transitive Point-primitive Symmetric Designs and Three Dimensional Projective Special Linear Groups
نویسندگان
چکیده
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).
منابع مشابه
Flag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups
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).
متن کاملFlag-transitive point-primitive $(v,k,4)$ symmetric designs with exceptional socle of Lie type
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.
متن کاملOn primitivity and reduction for flag-transitive symmetric designs
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 ...
متن کاملFlag-transitive non-symmetric 2-designs with (r, λ) = 1 and alternating socle
This paper deals with flag-transitive non-symmetric 2-designs with (r, λ) = 1. We prove that if D is a non-trivial non-symmetric 2-(v, k, λ) design with (r, λ) = 1 and G 6 Aut(D) is flag-transitive with Soc(G) = An for n > 5, then D is a 2-(6, 3, 2) design, the projective space PG(3, 2), or a 2-(10, 6, 5) design.
متن کاملPermutations Which Make Transitive Groups Primitive
In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating gr...
متن کامل