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In this paper we study the classification of right-angled Artin groups up to commensurability. We characterise the commensurability classes of RAAGs defined by trees of diameter 4. In particular, we prove a conjecture of Behrstock and Neumann that there are infinitely many commensurability classes of such RAAGs.
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Montserrat Casals-Ruiz, Ilya Kazachkov, Alexander Zakharov, On commensurability of right-angled Artin groups I: RAAGs defined by trees of diameter 4. Rev. Mat. Iberoam. 35 (2019), no. 2, pp. 521–560DOI 10.4171/RMI/1061