Related papers: Locally primitive block designs

An endomorphism of a free group is called primitivity preserving if it takes every primitive element to another primitive. In this paper we prove that every primitivity preserving endomorphism of a free group of a finite rank n > 2 is an…

We prove a local-to-global result for fixed points of groups acting on affine buildings (possibly non-discrete) of types $\tilde{A}_2$ or $\tilde{C}_2$. In the discrete case, our theorem establishes the corresponding special cases of a…

We introduce the notion of primitive elements in arbitrary truncated $p$-divisible groups. By design, the scheme of primitive elements is finite and locally free over the base. Primitive elements generalize the "points of exact order $N$,"…

More than $30$ years ago, Delandtsheer and Doyen showed that the automorphism group of a block-transitive $2$-design, with blocks of size $k$, could leave invariant a nontrivial point-partition, but only if the number of points was bounded…

Let $G$ be a finite primitive permutation group on a set $\Omega$ with nontrivial point stabilizer $G_{\alpha}$. We say that $G$ is extremely primitive if $G_{\alpha}$ acts primitively on each of its orbits in $\Omega \setminus \{\alpha\}$.…

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 partial linear space is a pair $(\mathcal{P},\mathcal{L})$ where $\mathcal{P}$ is a non-empty set of points and $\mathcal{L}$ is a collection of subsets of $\mathcal{P}$ called lines such that any two distinct points are contained in at…

This paper deals essentially with affine or projective transformations of Lie groups endowed with a flat left invariant affine or projective structure. These groups are called flat affine or flat projective Lie groups. Our main results…

We classify all spherical 2-designs that arise as orbits of finite group actions on real inner product spaces. Although it is well known that such designs can occur in representations without trivial components, we give a complete…

We consider 2-local geometries and other subgroup complexes for sporadic simple groups. For six groups, the fixed point set of a noncentral involution is shown to be equivariantly homotopy equivalent to a standard geometry for the component…

The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper shows that the study of locally s-distance transitive graphs…

The Clifford group is the quotient of the normalizer of the Weyl-Heisenberg group in dimension $d$ by its centre. We prove that when $d$ is not prime the Clifford group is not a group unitary $2$-design. Furthermore, we prove that the…

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…

The present paper is devoted to local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We prove that all local derivations and 2-local derivations on a finite-dimensional complex simple Leibniz…

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…

Let $G$ be a group of collineations of a finite thick generalised quadrangle $\Gamma$. Suppose that $G$ acts primitively on the point set $\mathcal{P}$ of $\Gamma$, and transitively on the lines of $\Gamma$. We show that the primitive…

Let G be a finite group and let p be a prime. A module for G over a field of characteristic p is called algebraic if it satisfies a polynomial, with addition and multiplication given by direct sum and tensor product. In some sense, having…

We show that the group of type-preserving automorphisms of any irreducible semi-regular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated (abstractly)…

We classify principal $2$-blocks of finite groups $G$ with Sylow $2$-subgroups isomorphic to a wreathed $2$-group $C_{2^n}\wr C_2$ with $n\geq 2$ up to Morita equivalence and up to splendid Morita equivalence. As a consequence, we obtain…

The classification of the finite primitive permutation groups of rank $3$ was completed in the 1980s and this landmark achievement has found a wide range of applications. In the general transitive setting, a classical result of Higman shows…