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arXiv · 2003.05531

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

Pallavi Dani·Ivan Levcovitz
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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 non-planar 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.

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Pallavi Dani, Ivan Levcovitz. 2020-03-11. Right-angled Artin subgroups of right-angled Coxeter and Artin groups. https://doi.org/10.2140/agt.2024.24.755

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