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arXiv · 1505.02053

Hyperbolic diagram groups are free

Anthony Genevois
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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.

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Anthony Genevois. 2015-05-08. Hyperbolic diagram groups are free. https://arxiv.org/abs/1505.02053

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