相关论文: Virtual splittings of right-angled Artin groups

Let $\Gamma$ be a connected, triangle-free, planar graph with at least five vertices that has no separating vertices or edges. If the graph $\Gamma$ is $\mathcal{CFS}$, we prove that the right-angled Coxeter group $G_\Gamma$ is virtually a…

A $\Gamma$\emph{-distance magic labeling} of a graph $G = (V, E)$ with $|V| = n$ is a bijection $\ell$ from $V$ to an Abelian group $\Gamma$ of order $n$, for which there exists $\mu \in \Gamma$, such that the weight $w(x) =\sum_{y\in…

The present article continues the study of median groups initiated in [6, 9, 10]. Some classes of median groups are introduced and investigated with a stress upon the class of the so called A-groups which contains as remarkable subclasses…

This article focuses on finding the eigenvalues of the Laplacian matrix of the comaximal graph $\Gamma(\mathbb Z_n)$ of the ring $\mathbb Z_n$ for $n> 2$. We determine the eigenvalues of $\Gamma(\mathbb Z_n)$ for various $n$ and also…

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually free group…

Given a right-angled Artin group $G$ with finite outer automorphism group, we determine which right-angled Artin groups are measure equivalent (or orbit equivalent) to $G$.

For a crystal group $\Gamma$ in dimension $n$, a closed subspace $\mathcal{V}$ of $L^2(\mathbb{R}^n)$ is called $\Gamma$--shift invariant if, for every $f\in\mathcal{V}$, the shifts of $f$ by every element of $\Gamma$ also belong to…

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…

The following problem has been known since the 80s. Let $\Gamma$ be an Abelian group of order $m$ (denoted $|\Gamma|=m$), and let $t$ and $\{m_i\}_{i=1}^{t}$, be positive integers such that $\sum_{i=1}^t m_i=m-1$. Determine when…

We study atomic right-angled Artin groups -- those whose defining graph has no cycles of length less than five, and no separating vertices, separating edges, or separating vertex stars. We show that these groups are not quasi-isometrically…

We prove that an arbitrary right-angled Artin group $G$ admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequently, $G$ admits quasi-isometric group embeddings into a pure…

A result of Baumslag and Roseblade states that a finitely presented subgroup of the direct product of two free groups is virtually a direct product of free groups. In this paper we generalise this result to the class of cyclic subgroup…

We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of…

We determine the factorial growth rate of the number of finite index subgroups of right-angled Artin groups as a function of the index. This turns out to depend solely on the independence number of the defining graph. We also make a…

Outer automorphism groups of RAAGs, denoted $Out(A_\Gamma)$, interpolate between $Out(F_n)$ and $GL_n(\mathbb{Z})$. We consider several vastness properties for which $Out(F_n)$ behaves very differently from $GL_n(\mathbb{Z})$: virtually…

The aim of this paper is to study the intersection hypergraph $\tilde{\Gamma}_\mathcal{H}(\mathbb{Z}_n)$ and co-maximal hypergraph $Co_\mathcal{H}(\mathbb{Z}_n)$ on the subgroups of $\mathbb{Z}_n$. We prove that the intersection and…

Let F be a finite field. We prove that the cohomology algebra with coefficients in F of a right-angled Artin group is a strongly Koszul algebra for every finite graph ${\Gamma}$. Moreover, the same algebra is a universally Koszul algebra…

This paper is a new contribution to the study of regular subgroups of the affine group $AGL_n(F)$, for any field $F$. In particular we associate to any partition $\lambda\neq (1^{n+1})$ of $n+1$ abelian regular subgroups in such a way that…

Let $\Gamma\subset \bar{\mathbb{Q}}^*$ be a finitely generated subgroup. Denote by $\Gamma_\mathrm{div}$ its division group. A recent conjecture due to R\'emond, related to the Zilber-Pink conjecture, predicts that the absolute logarithmic…

We provide a summary of research on disjoint zero-sum subsets in finite Abelian groups, which is a branch of additive group theory and combinatorial number theory. An orthomorphism of a group $\Gamma$ is defined as a bijection $\varphi$…