Related papers: The structure of $3$-pyramidal groups

We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these "twisted" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of…

We present a framework that connects three interesting classes of groups: the twisted groups (also known as Suzuki-Ree groups), the mixed groups and the exotic pseudo-reductive groups. For a given characteristic p, we construct categories…

It is proved that a three-dimensional double cone is a birationally rigid variety. We also compute the group of birational automorphisms of such a variety. This work is based on the method of "untwisting" maximal singularities of linear…

From a recent perspective, the structure of a 3-connected graph is studied in this paper. It stipulates the minimum dominating set of a 3-connected graph. Also, we count the number of structures, as a consequence, the upper bound is…

We prove that if a group scheme of multiplicative type acts on an algebraic stack with affine, finitely presented diagonal then the stack of fixed points is algebraic. For this, we extend two theorems of [SGA3.2] on functors of subgroups of…

Let $G$ be a finite group, and let $\Delta(G)$ be the prime graph built on its set of conjugacy class sizes: this is the (simple undirected) graph whose vertices are the prime numbers dividing some conjugacy class size of $G$, and two…

The purpose of this paper is to classify all pairs $(\mathcal{D}, G)$, where $\mathcal{D}$ is a non-trivial $2$-$(v, k, 2)$ design, and $G\leq Aut(\mathcal{D})$ acts transitively on the set of blocks of $\mathcal{D}$ and primitively on the…

A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points such that every two blocks intersect each other in $\lambda$ points (and $\lambda < v$ is a fixed number) and…

This is an expository work presenting in detail the proof of the structure theorem for divisible abelian groups. A divisible abelian group is an abelian group that satisfies nD=D for all natural n. The theorem states that any divisible…

We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a given rectangular prism and of minimal volume…

From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of…

The structure of the character degree graphs $\Delta(G)$, i.e. the prime graphs on the set $\mathrm{cd}(G)$ of the irreducible character degrees of a finite group $G$, such that $G$ is solvable and $\Delta(G)$ has diameter three, remains an…

It was shown in 1989 by Delandtsheer and Doyen that, for a $2$-design with $v$ points and block size $k$, a block-transitive group of automorphisms can be point-imprimitive (that is, leave invariant a nontrivial partition of the point set)…

A complex orthogonal (geometric) structure on a complex manifold is a geometric structure locally modelled on a non-degenerate quadric. One of the first examples of such a structure on a compact manifold of dimension three was constructed…

We study the structure of combinatorial Burnside groups, which receive equivariant birational invariants of actions of finite groups on algebraic varieties.

We determine which simple algebraic groups of type $^3D_4$ over arbitrary fields of characteristic different from 2 admit outer automorphisms of order 3, and classify these automorphisms up to conjugation. The criterion is formulated in…

Following the general strategy proposed by G.Rybnikov, we present a proof of his well-known result, that is, the existence of two arrangements of lines having the same combinatorial type, but non-isomorphic fundamental groups. To do so, the…

Let M denote either Euclidean or hyperbolic n-space, and let G be a discrete group of isometries of M, with the property that G respects and acts tile-transitively on a convex-polyhedral tesselation of M. Given an arbitrary base point p in…

Unimodal (i.e. single-humped) permutations may be decomposed into a product of disjoint cycles. Some enumerative results concerning their cyclic structure -- e.g. 2/3 of them contain fixed points -- are given. We also obtain in effect a…

We define the triple Riordan group, whose elements consist of $4$-tuples of power series $(g, f_1, f_2, f_3)$ with $g\in \mathbf{R}[[x^3]]$, and $f_1, f_2, f_3 \in x\mathbf{R}[[x^3]]$, for an appropriate ring $\mathbf{R}$. The construction…