On commuting elements and embeddings of graph groups and monoids

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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.
14 pages, 1 figure, typos fixed, introduction improved slightly, results unchanged

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Group Theory, 20F36, 20M05

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http://salesiana.dossiersoluciones.com/handle/123456789/107373

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601042
 http://arxiv.org/abs/math/0601042

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arXiv