Related papers: The Higman-M\lowercase{c}Laughlin Theorem for the …

Let $G$ be a flag-transitive automorphism group of a $(v,k,\lambda)$ symmetric design $\mathcal{D}$ with $k>\lambda(\lambda-2)$. O'Reilly Regueiro proved that if $G$ is point-imprimitive, then $\mathcal{D}$ has parameters…

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 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…

In this paper, we present a classification of $2$-designs with $\gcd(r,\lambda)=1$ admitting flag-transitive automorphism groups. If $G$ is a flag-transitive automorphism group of a non-trivial $2$-design $\mathcal{D}$ with…

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…

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…

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 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,…

In 1987, Huw Davies proved that, for a flag-transitive point-imprimitive $2$-$(v,k,\lambda)$ design, both the block-size $k$ and the number $v$ of points are bounded by functions of $\lambda$, but he did not make these bounds explicit. In…

In this article, we investigate symmetric 2-designs of prime order admitting a flag-transitive automorphism group G. Recently, the authors proved that the automorphism group G of this type of designs must be point-primitive, and is of…

In this article, we study $2$-designs with $\lambda=2$ admitting a flag-transitive almost simple automorphism group with socle a finite simple exceptional group of Lie type, and we prove that such a $2$-design does not exist. In conclusion,…

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…

In this article, we study $2$-designs with prime replication number admitting a flag-transitive automorphism group. The automorphism groups of these designs are point-primitive of almost simple or affine type. We determine $2$-designs with…

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 $G$…

It is shown that, apart from the smallest Ree group, a flag-transitive automorphism group $G$ of a $2$-$(k^{2}, k, \lambda)$ design D, with $\lambda \mid k$, is either an affine group or an almost simple classical group. Moreover, when $G$…

In this paper we develop several general methods for analysing flag-transitive point-imprimitive $2$-designs, which give restrictions on both the automorphisms and parameters of such designs. These constitute a tool-kit for analysing these…

Let $\mathcal{D} = (\mathcal{P}, \mathcal{B})$ be a $2$-$(v, k, \lambda)$ design, and let $G$ be a half-flag-transitive automorphism group of ${\cal D}$. In this article, we first establish three sufficient conditions for $G$ to be…

We give a construction of a family of designs with a specified point-partition, and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in the family to…