Related papers: Doubly transitive lines II: Almost simple symmetri…

The main result of the present paper is a construction of relative moduli spaces of stable sheaves over the stack of quasipolarized projective surfaces. For this, we use the theory of good moduli spaces, whose study was initiated by Alper.…

The paper discusses stably trivial torsors for spin and orthogonal groups over smooth affine schemes over infinite perfect fields of characteristic unequal to 2. We give a complete description of all the invariants relevant for the…

For quasifields, the concept of parastrophy is slightly weaker than isotopy. Parastrophic quasifields yield isomorphic translation planes but not conversely. We investigate the right multiplication groups of finite quasifields. We classify…

We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover we prove that the same holds with self-dual in place of symmetric. The…

For each finite classical group $G$, we classify the subgroups of $G$ which act transitively on a $G$-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the…

Ostrom and Wagner (1959) proved that if the automorphism group $G$ of a finite projective plane $\pi$ acts $2$-transitively on the points of $\pi$, then $\pi$ is isomorphic to the Desarguesian projective plane and $G$ is isomorphic to…

Let $\mathcal{D}$ be a non-trivial quasi-symmetric $2$-design with two block intersection numbers $x=0$ and $2\leq y\leq10$, and suppose that $G$ is an automorphism group of $\mathcal{D}$. If $G$ is flag-transitive and point-primitive, then…

Planar locally finite graphs which are almost vertex transitive are discussed. If the graph is 3-connected and has at most one end then the group of automorphisms is a planar discontinuous group and its structure is well-known. A general…

A weak pseudoline arrangement is a topological generalization of a line arrangement, consisting of curves topologically equivalent to lines that cross each other at most once. We consider arrangements that are outerplanar---each crossing is…

We investigate algebraic and topological transitivity and, more generally, k-transitivity for linear spaces of operators. In finite dimensions, we determine minimal dimensions of k-transitive spaces for every k, and find relations between…

This is the second of a series of papers which aim towards a classification of edge-transitive maps of which the Euler characteristic and the edge number are coprime. This one carries out the classification work for arc-transitive maps with…

The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are…

We initiate the study of $\xi$-groups and Hu-Liu Leibniz algebras, claim that alomost all simple Leibniz algebras and simple Hu-Liu Leibniz algebras are linear, and establish two passages. One is the passage from a special…

We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.

In the present note we study combinatorial and algebraic properties of cubic-line arrangements in the complex projective plane admitting nodes, ordinary triple and $A_{5}$ singular points. We deliver a Hirzebruch-type inequality for such…

We provide a classification result on nearly free arrangements of lines in the complex projective plane with nodes and triple points.

Finite covers are a technique for building new structures from simpler ones. The original motivation to study finite covers is in the Ladder theorem of Zilber which describes how totally categorical structures are built from strictly…

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…

The semidirect product of a finitely generated group dual with the symmetric group can be described through so-called group-theoretical categories of partitions (covers only a special case; due to Raum--Weber, 2015) and skew categories of…

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…