Anthony Genevois
Published 2015-05-08Version 1
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.
Comments: 17 pages, 9 figures
The geometry of one-relator groups satisfying a polynomial isoperimetric inequality
Morphisms between right-angled Coxeter groups: the two-dimensional case
Free Groups in Lattices
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