Related papers: Symmetric designs and projective special unitary g…

In this article, we study symmetric $(v, k, \lambda)$ designs admitting a flag-transitive and point-primitive automorphism group $G$ whose socle is $PSU_{4}(q)$. We prove that there exist eight non-isomorphic such designs for which…

Let $\mathcal D$ be a nontrivial symmetric $(v,k,\lambda)$ design, and $G$ be a subgroup of the full automorphism group of $\mathcal D$. In this paper we prove that if $G$ acts flag-transitively, point-primitively on $\mathcal D$ and…

In this article, we study symmetric $(v, k, \lambda)$ designs admitting a flag-transitive and point-primitive automorphism group $G$ whose socle $X$ is a finite simple exceptional group of Lie type. We prove a reduction theorem, severely…

In this article, we study flag-transitive automorphism groups of non-trivial symmetric $(v, k, \lambda)$ designs, where $\lambda$ divides $k$ and $k\geq \lambda^2$. We show that such an automorphism group is either point-primitive of affine…

The symmetric $2$-$(v,k,\lambda )$ designs, with $k>\lambda \left(\lambda-3 \right)/2$, admitting a flag-transitive, point-imprimitive automorphism group are completely classified: they are the known $2$-designs with parameters…

In this article, we investigate symmetric $(v,k,\lambda)$ designs $\mathcal{D}$ with $\lambda$ prime admitting flag-transitive and point-primitive automorphism groups $G$. We prove that if $G$ is an almost simple group with socle a finite…

In this article, we investigate symmetric designs admitting a flag-transitive and point-primitive affine automorphism group. We prove that if an automorphism group $G$ of a symmetric $(v,k,\lambda)$ design with $\lambda$ prime is…

In this article, we study $2$-$(v,k,\lambda)$ designs $\mathcal{D}$ with $\lambda$ prime admitting flag-transitive and point-primitive almost simple automorphism groups $G$ with socle $T$ a finite exceptional simple group or a sporadic…

In this article, we study $2$-designs with $\gcd(r, \lambda)=1$ admitting a flag-transitive automorphism group. The automorphism groups of these designs are point-primitive of almost simple or affine type. We determine all pairs…

This paper is devoted to the classification of all flag-transitive point-primitive non-trivial $2$-$(v, k, \lambda)$ designs with the alternating group $A_n$($n \le 10$) as the socle of their automorphism groups, and 87 different designs…

In this article, we investigate $2$-$(v,k,\lambda)$ designs with $\gcd(r,\lambda)=1$ admitting flag-transitive automorphism groups $G$. We prove that if $G$ is an almost simple group, then such a design belongs to one of the seven infinite…

This paper studies flag-transitive point-primitive non-symmetric $2$-($v,k,2$) designs. We prove that if $\mathcal{D}$ is a non-trivial non-symmetric $2$-$(v,k,2)$ design admitting a flag-transitive point-primitive automorphism group $G$…

This paper determined all pairs $(\mathcal{D},G)$ where $\mathcal{D}$ is a non-symmetric 2-$(v,k,\lambda)$ design with $(r,\lambda)=1$ and $G$ is the almost simple flag-transitive automorphism group of $\mathcal{D}$ with an exceptional…

In this article, we study symmetric designs admitting flag-transitive, point-imprimitive almost simple automorphism groups with socle sporadic simple groups. As a corollary, we present a classification of symmetric designs admitting…

Let $\mathcal{D}=\left(\mathcal{P},\mathcal{B} \right)$ be a symmetric $2$-$(v,k,\lambda )$ design admitting a flag-transitive, point-imprimitive automorphism group $G$ that leaves invariant a non-trivial partition $\Sigma$ of…

A complete classification of the flag-transitive point-imprimitive symmetric $2$-$(v,k,\lambda )$ designs with $v<100$ is provided. Apart from the known examples with $\lambda \leq 10$, the complementary design of $PG_{5}(2)$, and the…

This paper is devoted to the study of $2$-designs with $\lambda\ge (r,\lambda)^2$ admitting a flag-transitive automorphism group $G$. The group $G$ has been shown to be point-primitive of either almost simple or affine type. In this paper,…

This paper investigates block-transitive automorphism groups of t-(k^2,k,\lambda) designs. Let D be a non-trivial t-(k^2,k,\lambda) design, G \leq \Aut(D) be block-transitive with X\unlhd G\leq \Aut(X), where X = PSL(2,q)(q\geq4). Then 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 flag-transitive subgroup G of the automorphism group of a nontrivial 2-(v,k,2) design is…

This paper investigates $2$-$(v,5,\lambda)$ designs $\mathcal{D}$ admitting a block-transitive automorphism group $G$. We first prove that if $G$ is point-imprimitive, then $v$ must be one of 16, 21, or 81. We further provide a complete…