Hyperbolic diagram groups are free

Abstract

In this paper, we study the so-called diagram groups. Our main result is that diagram groups are free if and only if they do not contain any subgroup isomorphic to ${\mathbb{Z}}^2$. As an immediate corollary, we get that hyperbolic diagram groups are necessarily free, answering a question of Guba and Sapir.

17 pages, 9 figures

References in corpus (1)

• Surface subgroups of right-angled Artin groups