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On commuting elements and embeddings of graph groups and monoids

Mark Kambites
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Abstract

We study commutation properties of subsets of right-angled Artin groups and trace monoids. We show that if Gamma is any graph not containing a four-cycle without chords, then the group G(Gamma) does not contain four elements whose commutation graph is a four-cycle; a consequence is that G(Gamma) does not have a subgroup isomorphic to a direct product of non-abelian free groups. We also obtain corresponding and more general results for monoids.

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Mark Kambites. 2006-02-03. On commuting elements and embeddings of graph groups and monoids. https://arxiv.org/abs/math/0601042

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