On conjugacy separability of graph products of groups

Abstract

We show that the class of $\mathcal{C}$-hereditarily conjugacy separable groups is closed under taking arbitrary graph products whenever the class $\mathcal{C}$ is an extension closed variety of finite groups. As a consequence we show that the class of $\mathcal{C}$-conjugacy separable groups is closed under taking arbitrary graph products. In particular, we show that right angled Coxeter groups are hereditarily conjugacy separable and 2-hereditarily conjugacy separable, and we show that infinitely generated right angled Artin groups are hereditarily conjugacy separable and $p$-hereditarily conjugacy separable for every prime number $p$.

40 pages

Cited by in corpus (8)

• Separating cyclic subgroups in graph products of groups
• On conjugacy separability of fibre products
• Conjugacy languages in virtual graph products
• Outer automorphism groups of graph products: subgroups and quotients
• Residual properties of graph products of groups
• Limit Groups are Subgroup Conjugacy Separable
• Bounding conjugacy depth functions for wreath products of finitely generated abelian groups
• Separability properties of automorphisms of graph products of groups