Related papers: Subgroups of Bestvina-Brady groups

A finitely presented Bestvina-Brady group (BBG) admits a presentation involving only commutators. We show that if a graph admits a certain type of spanning trees, then the associated BBG is a right-angled Artin group (RAAG). As an…

Right-angled Artin groups and their subgroups are of great interest because of their geometric, combinatorial and algorithmic properties. It is convenient to define these groups using finite simplicial graphs. The isomorphism type of the…

We compute the relative divergence and the subgroup distortion of Bestvina-Brady subgroups. We also show that for each integer $n\geq 3$, there is a free subgroup of rank $n$ of some right-angled Artin group whose inclusion is not a…

Let $p$ be a prime. The right-angled Artin pro-$p$ group $G_{\Gamma}$ associated to a fnite simplicial graph $\Gamma$ is the pro-$p$ completion of the right-angled Artin group associated to $\Gamma$. We prove that the following assertions…

We generalize to (certain) Artin groups some results previously known for right-angled Artin groups (RAAGs). First, we generalize a result by Droms, B. Servatius, and H. Servatius, and prove that the derived subgroup of an Artin group is…

We show that if a right-angled Artin group $A(\Gamma)$ has a non-trivial, minimal action on a tree $T$ which is not a line, then $\Gamma$ contains a separating subgraph $\Lambda$ such that $A(\Lambda)$ stabilizes an edge in $T$.

We characterize twisted right-angled Artin groups (T-RAAGs) that are subgroup separable using only their defining mixed graphs: such a group is subgroup separable if and only if the underlying simplicial graph contains neither induced paths…

Koberda proved that if a graph $\Gamma$ is a full subgraph of a curve graph $\mathcal{C}(S)$ of an orientable surface $S$, then the right-angled Artin group $A(\Gamma)$ on $\Gamma$ is a subgroup of the mapping class group ${\rm Mod}(S)$ of…

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…

Let $N$ be a closed nonorientable surface with or without marked points. In this paper we prove that, for every finite full subgraph $\Gamma$ of $\mathcal{C}^{\mathrm{two}}(N)$, the right-angled Artin group on $\Gamma$ can be embedded in…

We determine when certain natural classes of subgroups of right-angled Coxeter groups (RACGs) and right-angled Artin groups (RAAGs) are themselves RAAGs. We characterize finite-index visual RAAG subgroups of 2-dimensional RACGs. As an…

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…

For a finite graph $\Gamma$, let $G(\Gamma)$ be the right-angled Artin group defined by the complement graph of $\Gamma$. We show that, for any linear forest $\Lambda$ and any finite graph $\Gamma$, $G(\Lambda)$ can be embedded into…

We show that for a sufficiently simple surface $S$, a right-angled Artin group $A(\Gamma)$ embeds into $\Mod(S)$ if and only if $\Gamma$ embeds into the curve graph $\mC(S)$ as an induced subgraph. When $S$ is sufficiently complicated,…

Bestvina-Brady groups arise as kernels of length homomorphisms from right-angled Artin groups G_\G to the integers. Under some connectivity assumptions on the flag complex \Delta_\G, we compute several algebraic invariants of such a group…

Let $\Gamma$ be a simplicial, finite, connected graph such that $\Gamma$ does not decompose as a nontrivial join. We prove that two notions of strong quasiconvexity and stability are equivalent in the right-angled Artin group $A_\Gamma$…

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.…

For a prime number $\ell$ we introduce and study oriented right-angled Artin pro-$\ell$ groups $G_{\Gamma,\lambda}$(oriented pro-$\ell$ RAAGs for short) associated to a finite oriented graph $\Gamma$ and a continuous group homomorphism…

A result of Bridson, Howie, Miller and Short states that if $S$ is a subgroup of type $FP_{n}(\mathbb{Q})$ of the direct product of $n$ limit groups over free groups, then $S$ is virtually the direct product of limit groups over free…

We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups…