#### Volume 14, issue 3 (2014)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
Algebraic ranks of $\mathrm{CAT}(0)$ groups

### Raeyong Kim

Algebraic & Geometric Topology 14 (2014) 1627–1648
##### Abstract

We study the algebraic rank of various classes of $CAT\left(0\right)$ groups. They include right-angled Coxeter groups, right-angled Artin groups, relatively hyperbolic groups and groups acting geometrically on $CAT\left(0\right)$ spaces with isolated flats. As one of our corollaries, we obtain a new proof of a result on commensurability of Coxeter groups.

##### Keywords
algebraic rank of a group, $\mathrm{CAT}(0)$ groups, right-angled Coxeter groups, relatively hyperbolic groups
##### Mathematical Subject Classification 2010
Primary: 57M07
Secondary: 20F55, 20F65