Related papers: Right Angled Artin Groups and partial commutation,…

We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew) commutative algebra of squarefree…

We give an explicit formula for the cohomology of a right angled Artin group with group ring coefficients in terms of the cohomology of its defining flag complex.

We use polyhedral product models to analyse the structure of the commutator subgroup of a right-angled Artin group. In particular, we provide a minimal set of generators for the commutator subgroup, consisting of special iterated…

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…

For any prime $p$ and group $G$, denote the pro-$p$ completion of $G$ by $\hat{G}^p$. Let $\mathcal{C}$ be the class of all groups $G$ such that, for each natural number $n$ and prime number $p$, $H^n(\hat{G^p},\mathbb Z/p)\cong H^n(G,…

Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…

Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications.…

We compute the group homology, the algebraic $K$- and $L$-groups, and the topological $K$-groups of right-angled Artin groups, right-angled Coxeter groups, and more generally, graph products.

We prove that every right-angled Artin group occurs as a finite-index subgroup of the outer automorphism group of another right-angled Artin group. We furthermore show that the latter group can be chosen in such a way that the quotient is…

According to the Tits conjecture proved by Crisp and Paris, [CP], the subgroups of the braid group generated by proper powers of the Artin elements are presented by the commutators of generators which are powers of commuting elements. Hence…

Given a finite graph G there is a corresponding group given by the presentation with generators the vertices of G and a relation [x,y]=1 for generators x and y precisely when (x,y) is an edge of G. Such groups are known as partially…

We prove an analogue of the L\"uck Approximation Theorem in positive characteristic for certain residually finite rationally soluble (RFRS) groups including right-angled Artin groups and Bestvina--Brady groups. Specifically, we prove that…

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…

We construct and study polyhedral product models for classifying spaces of right-angled Artin and Coxeter groups, general graph product groups and their commutator subgroups. By way of application, we give a criterion of freeness for the…

The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…

We determine the central extensions of a whole family of Lie algebras, obtained by the method of graded contractions from so(N+1), N arbitrary. All the inhomogeneous orthogonal and pseudo-orthogonal algebras are members of this family, as…

In this note we give the quasi-isometry classification for a class of right angled Artin groups. In particular, we obtain the first such classification for a class of Artin groups with dimension larger than 2; our families exist in every…

We prove that every subnormal subgroup of p-power index in a right-angled Artin group is conjugacy p-separable. As an application, we prove that every right-angled Artin group is conjugacy separable in the class of torsion-free nilpotent…

We characterize twisted right-angled Artin groups whose finitely generated subgroups are also twisted right-angled Artin groups. Additionally, we give a classification of coherence within this class of groups in terms of the defining graph.…

We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal…