Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Right-angled Artin subgroups of right-angled Coxeter and Artin groups

Pallavi Dani and Ivan Levcovitz

Algebraic & Geometric Topology 24 (2024) 755–802
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

Open Access made possible by participating institutions via Subscribe to Open.