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Right-angled Artin subgroups of right-angled Coxeter and Artin groups

Pallavi Dani and Ivan Levcovitz

Algebraic & Geometric Topology 24 (2024) 755–802

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.

right-angled Artin group, right-angled Coxeter group, commensurable
Mathematical Subject Classification
Primary: 20F55, 20F65
Received: 2 September 2020
Revised: 6 July 2022
Accepted: 19 September 2022
Published: 12 April 2024
Pallavi Dani
Department of Mathematics
Louisiana State University
Baton Rouge, LA
United States
Ivan Levcovitz
Department of Mathematics
Tufts University
Medford, MA
United States

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