Related papers: Block-transitive and point-primitive $2$-$(v,k,2)$…

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 symmetric $(v, k, \lambda)$ designs admitting a flag-transitive and point-primitive automorphism group $G$ whose socle is a projective special unitary group of dimension at most five. We, in particular, determine…

Let $\mathcal{D}$ be a block design admitting a locally transitive automorphism group $G$. We say that $\mathcal{D}$ is $G$-point-locally dihedral if the induced local action $G_x^{\mathcal{D}}$ is dihedral for each point $x$, and that…

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…

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…

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 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…

Suppose that an automorphism group $G$ acts flag-transitively on a finite generalized hexagon or octagon $\cS$, and suppose that the action on both the point and line set is primitive. We show that $G$ is an almost simple group of Lie type,…

In this paper, we study the primitive actions of almost simple exceptional groups of Lie type on \(s\)-arc-transitive digraphs. Our motivation is the following question posed by Giudici and Xia: Is there an upper bound on $s$ for finite…

We view a design $\mathcal{D}$ as a set of $k$-subsets of a fixed set $X$ of $v$ points. A $k$-subset of $X$ is at distance $i$ from $\mathcal{D}$ if it intersects some $k$-set in $\mathcal{D}$ in $k-i$ points, and no subset in more than…

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…

Block-transitive Steiner $t$-designs form a central part of the study of highly symmetric combinatorial configurations at the interface of several disciplines, including group theory, geometry, combinatorics, coding and information theory,…

Let $K$ be the function field of a $p$-adic curve, $G$ a semisimple simply connected group over $K$ and $X$ a $G$-torsor over $K$. A conjecture of Colliot-Th\'el\`ene, Parimala and Suresh predicts that if for every discrete valuation $v$ of…

In this paper we show that a flag-transitive automorphism group $G$ of a non-trivial $2$-$(v,k,\lambda)$ design with $\lambda\geq (r, \lambda)^2$ is not of product action type. In conclusion, $G$ is a primitive group of affine or almost…

The first main result of this paper is that a finite transitive nonabelian characteristically simple subgroup of a wreath product in product action must lie in the base group of the wreath product. This allows us to characterize nonabelian…

A graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let $\Gamma$ be a connected graph…

Given a transitive permutation group G of degree n , we seek to determine whether or not G is primitive, and to find a system of blocks of imprimitivity in the case that G is imprimitive. An algorithm of Atkinson solves this problem in time…

In this article we give self-contained existence proofs for the sporadic simple groups Co_2 and Fi_{22} using the second author's algorithm [10] constructing finite simple groups from irreducible subgroups of GL_n(2). These two sporadic…

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…

A locally primitive 2-design is a 2-design admitting an automorphism group $G$ with primitive local actions. It is proved that $G$ is point-primitive, and either $G$ is an almost simple group, or $G$ acting on the points is an affine group.