Document Type

Article

Publication Date

1-1-2024

Abstract

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 application, we show that any 2–dimensional, one-ended RACG with planar defining graph is quasi-isometric to a RAAG if and only if it is commensurable to a RAAG. Additionally, we give new examples of RACGs with nonplanar defining graphs which are commensurable to RAAGs. Finally, we give a new proof of a result of Dyer: every subgroup generated by conjugates of RAAG generators is itself a RAAG.

Publication Source (Journal or Book title)

Algebraic and Geometric Topology

First Page

755

Last Page

802

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