相关论文: On the elementary theory of graph products of grou…

We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…

A classical result of Schreier states that nontrivial finitely generated normal subgroups of free groups are of finite index, that is, free groups can only quotient to finite groups with finitely generated kernel. In this note we extend…

We prove three results about the graph product $G=\G(\Gamma;G_v, v \in V(\Gamma))$ of groups $G_v$ over a graph $\Gamma$. The first result generalises a result of Servatius, Droms and Servatius, proved by them for right-angled Artin groups;…

Suppose that $\Gamma$ is a non-empty connected graph, $\mathfrak{G}$ is the fundamental group of a graph of groups over $\Gamma$, and $\mathcal{C}$ is a root class of groups (the last means that $\mathcal{C}$ contains non-trivial groups and…

We study properties of automorphisms of graph products of groups. We show that graph product $\Gamma\mathcal{G}$ has non-trivial pointwise inner automorphisms if and only if some vertex group corresponding to a central vertex has…

We establish rigidity theorems for graph product von Neumann algebras $M_\Gamma=*_{v,\Gamma}M_v$ associated to finite simple graphs $\Gamma$ and families of tracial von Neumann algebras $(M_v)_{v\in\Gamma}$. We consider the following three…

We show that the outer automorphism groups of graph products of finitely generated abelian groups satisfy the Tits alternative, are residually finite, their so-called Torelli subgroups are finitely generated, and they satisfy a dichotomy…

In this paper we study the hyperbolicity properties of a class of random groups arising as graph products associated to random graphs. Recall, that the construction of a graph product is a generalization of the constructions of right-angled…

Let $G$ be a fundamental group of a graph of group where the graph is a rose or a star graph and the vertex groups are free groups, free abelian groups or right-angled Artin groups. We prove the linearity of $G$ over $\mathbb{Z}$ under…

Let $\Gamma$ be a finite graph and let $A(\Gamma)$ be the corresponding right-angled Artin group. From an arbitrary basis $\mathcal B$ of $H^1(A(\Gamma),\mathbb F)$ over an arbitrary field, we construct a natural graph $\Gamma_{\mathcal B}$…

The kernel of the natural projection of a graph product of groups onto their direct product is called the Cartesian subgroup of the graph product. This construction generalises commutator subgroups of right-angled Coxeter and Artin groups.…

We discuss various types of Tits Alternative for subgroups of graph products of groups, and prove that, under some natural conditions, a graph product of groups satisfies a given form of Tits Alternative if and only if each vertex group…

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 investigate criteria ensuring that a one-relator group $G$ contains a right-angled Artin subgroup $A(\Gamma)$, corresponding to a finite graph $\Gamma$. In particular, we prove that if $\Gamma$ is a forest with at least one edge and the…

A {\it graph product} $G$ on a graph $\Gamma$ is a group defined as follows: For each vertex $v$ of $\Gamma$ there is a corresponding non-trivial group $G_v$. The group $G$ is the quotient of the free product of the $G_v$ by the commutation…

We give a technical result that implies a straightforward necessary and sufficient conditions for a graph of groups with virtually cyclic edge groups to be one ended. For arbitrary graphs of groups, we show that if their fundamental group…

We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is…

We give a simpler proof using automata theory of a recent result of Kapovich, Weidmann and Myasnikov according to which so-called benign graphs of groups preserve decidability of the generalized word problem. These include graphs of groups…

Let $\mathcal{C}$ be a class of finite groups closed under taking subgroups, quotients, and extensions with abelian kernel. The right-angled Artin pro-$\mathcal{C}$ group $G_\Gamma$ (pro-$\mathcal{C}$ RAAG for short) is the…

A graph product kernel means the kernel of the natural surjection from a graph product to the corresponding direct product. We prove that a graph product kernel of countable groups is special, and a graph product of finite or cyclic groups…