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

Dani, Pallavi; Levcovitz, Ivan

doi:10.2140/agt.2024.24.755

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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

DOI: 10.2140/agt.2024.24.755

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.

Keywords

right-angled Artin group, right-angled Coxeter group, commensurable

Mathematical Subject Classification

Primary: 20F55, 20F65

References

Publication

Received: 2 September 2020

Revised: 6 July 2022

Accepted: 19 September 2022

Published: 12 April 2024

Authors

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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Volume 24, issue 2 (2024)