Related papers: Some new designs with prescribed automorphism grou…

This paper considers flag-transitive $4$-$(q+1,k,\lambda)$ designs with $\lambda\geq5$ and $q+1>k>4$. Let the automorphism group of a design $\cal D$ be a simple group $G=PSL(2,q)$. Depend on the fact that the setwise stabilizer $G_B$ must…

Computational techniques for the construction of quasi-symmetric block designs are explored and applied to the case with $56$ points. One new $(56,16,18)$ and many new $(56,16,6)$ designs are discovered, and non-existence of $(56,12,9)$ and…

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…

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…

The existence of a biplane with parameters $(121,16,2)$ is an open problem. Recently, it has been proved by Alavi, Daneshkhah and Praeger that the order of an automorphism group of a of possible biplane ${\mathcal D}$ of order $14$ divides…

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…

A design is called $t$-pyramidal when it has an automorphism group which fixes $t$ points and acts sharply transitively on the remaining points. We determine all symmetric $(2^k-1,2^{k-1},2^{k-2})$-designs which are $(2^{k-1}-1)$-pyramidal…

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…

In this paper we study the automorphism group of a possible symmetric $(81,16,3)$ design.

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 =…

The classification of the $2$-designs with $\lambda=2$ admitting a flag-transitive automorphism groups with socle $PSL(2,q)$ is completed by settling the two open cases in \cite{ABDT}. The result is achieved by using conics and hyperovals…

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…

The family of generalized Paley graphs of prime power order $q$ and degree $(q-1)/k$ is studied. It is shown that the automorphism group of a graph in this family is a subgroup of ${\mathrm{A\Gamma L}}(1,q)$ whenever $q$ is sufficiently…

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 paper we present a method for constructing directed strongly regular graphs with assumed action of an automorphism group. The application of this method leads to first examples of directed strongly regular graphs with parameters…

Given five positive integers $v, m,k,\lambda$ and $t$ where $v \geq k \geq t$ and $v \geq m \geq t,$ a $t$-$(v,k,m,\lambda)$ general covering design is a pair $(X,\mathcal{B})$ where $X$ is a set of $v$ elements (called points) and…

The paper shows the existence of a family of directed strongly regular graphs with parameters (22, 9, 6, 3, 4). The adjacency matrices of the found digraphs are composed of $3\times 3$ circulant blocks. The automorphism group of all the…

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…

In this paper, we provide a complete classification of the $2$-$(v,3,\lambda )$ designs with $v\equiv 1,3\pmod{6}$ and $% v \equiv 6 \pmod{\lambda}$ admitting a flag-transitive automorphism group non-isomorphic to a subgroup of $A\Gamma…

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…