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arXiv · 1803.00971

On commensurability of some right-angled Artin groups II: RAAGs defined by paths

Montserrat Casals-Ruiz·Ilya Kazachkov·Alexander Zakharov
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Abstract

In this paper we continue the study of right-angled Artin groups up to commensurability initiated in [CKZ]. We show that RAAGs defined by different paths of length greater than 3 are not commensurable. We also characterise which RAAGs defined by paths are commensurable to RAAGs defined by trees of diameter 4. More precisely, we show that a RAAG defined by a path of length $n>4$ is commensurable to a RAAG defined by a tree of diameter 4 if and only if $n$ is 2 modulo 4. These results follow from the connection that we establish between the classification of RAAGs up to commensurability and linear integer-programming.

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Montserrat Casals-Ruiz, Ilya Kazachkov, Alexander Zakharov. 2018-03-02. On commensurability of some right-angled Artin groups II: RAAGs defined by paths. https://arxiv.org/abs/1803.00971

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