Related papers: Classification of the non-trivial $2$-$(k^{2},k,\l…

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 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…

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 =…

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…

Let $\mathcal{D}$ be a nontrivial $3$-$(v,k,1)$ design admitting a block-transitive group $G$ of automorphisms. A recent work of Gan and the second author asserts that $G$ is either affine or almost simple. In this paper, it is proved that…

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…

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…

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…

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…

We solve the long-standing open problem of classifying all 3-(v,k,1) designs with a flag-transitive group of automorphisms (cf. A. Delandtsheer, Geom. Dedicata 41 (1992), p. 147; and in: "Handbook of Incidence Geometry", ed. by F.…

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…

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…

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently…

In this article, we prove that if $\mathcal{D}$ is a $2$-design with $k=7$ admitting flag-transitive almost simple automorphism group with socle an alternating group, then $\mathcal{D}$ is $PG_{2}(3,2)$ with parameter set $(15,7,3)$ and…

Given an integer $k\ge3$ and a group $G$ of odd order, if there exists a $2$-$(v,k,1)$-design and if $v$ is sufficiently large, then there is such a design whose automorphism group has a subgroup isomorphic to $G$. A weaker result is proved…

We announce the classification of two related classes of flag-transitive geometries. There is an infinite family of such geometries, related to the nonsplit extensions $3^{[{n\atop 2}]_{_2}}\cdot \SP_{2n}(2)$, and twelve sporadic examples…

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…

Let G be an automorphism group of a nontrivial t-(k^2,k,\lambda) design. In this paper, we prove that if G is block-transitive, then the socle of G cannot be a finite simple exceptional group of Lie type.