Related papers: The $R_\infty$-property for right-angled Artin gro…

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…

An element $g$ of a group $G$ is said to be right Engel if for every $x\in G$ there is a number $n=n(g,x)$ such that $[g,{}_{n}x]=1$. We prove that if a profinite group $G$ admits a coprime automorphism $\varphi$ of prime order such that…

We construct the first known examples of infinite subgroups of the outer automorphism group of Out(A_Gamma), for certain right-angled Artin groups A_Gamma. This is achieved by introducing a new class of graphs, called focused graphs, whose…

We introduce the palindromic automorphism group and the palindromic Torelli group of a right-angled Artin group A_G. The palindromic automorphism group Pi A_G is related to the principal congruence subgroups of GL(n,Z) and to the…

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 give a unified proof of property $R_\infty$ for the Higman groups $H_n$ ($n\ge 4$) and for their generalizations studied by Martin and Horbez--Huang. As a key step, we prove that the automorphism groups of these groups are acylindrically…

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…

For a finite simplicial graph $\Gamma$, let $A(\Gamma)$ denote the right-angled Artin group on $\Gamma$. Recently Kim and Koberda introduced the extension graph $\Gamma^e$ for $\Gamma$, and established the Extension Graph Theorem: for…

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 $G$ be a finitely generated polyfree group. If $G$ has nonzero Euler characteristic then we show that $Aut(G)$ has a finite index subgroup in which every automorphism has infinite Reidemeister number. For certain $G$ of length 2, we…

Let $G$ and $G'$ be two right-angled Artin groups (RAAG). We show they are quasi-isometric iff they are isomorphic, under the assumption that $Out(G)$ and $Out(G')$ are finite. If only $Out(G)$ is finite, then $G'$ is quasi-isometric $G$…

In this article, we consider qualified notions of geometric finiteness in mapping class groups called parabolically geometrically finite (PGF) and reducibly geometrically finite (RGF). We examine several constructions of subgroups and…

We prove that if $\mathbb{F}$ is an algebraically closed field of zero characteristic which has infinite transcendence degree over $\mathbb{Q}$, then there exists a field automorphism $\varphi$ of ${\rm SL}_n(\mathbb{F})$ and ${\rm…

In this article, we characterise geometrically when a right-angled Artin group splits over an abelian subgroup. More precisely, given a finite graph $\Gamma$, we show that $A(\Gamma)$ splits over an abelian subgroup if and only if it is…

We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group $A(\Gamma)$ fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups $\text{Mod}(S)$. In…

We describe the structure of virtually solvable normal subgroups in the automorphism group of a right-angled Artin group ${\rm Aut}(A_\Gamma)$. In particular, we prove that a finite normal subgroup in ${\rm Aut}(A_\Gamma)$ has at most order…

We prove a new version of the classical peak-reduction theorem for automorphisms of free groups in the setting of right-angled Artin groups. We use this peak-reduction theorem to prove two important corollaries about the action of the…

In this paper, generalising the idea of the Rokhlin property, we explore the concept of the twisted Rokhlin property of topological groups. A topological group is said to exhibit the twisted Rokhlin property if, for each automorphism $\phi$…

Let $R$ be a commutative ring with identity. We define a graph $\Gamma_{\aut}(R)$ on $ R$, with vertices elements of $R$, such that any two distinct vertices $x, y$ are adjacent if and only if there exists $\sigma \in \aut$ such that…

We study the (virtual) indicability of the automorphism group $Aut(A_\Gamma)$ of the right-angled Artin group $A_\Gamma$ associated to a simplicial graph $\Gamma$. First, we identify two conditions -- denoted (B1) and (B2) -- on $\Gamma$…