On commuting elements and embeddings of graph groups and monoids

Details On commuting elements and embeddings of graph groups and monoids On commuting elements and embeddings of graph groups and monoids

2006-01-03

arxiv.org/abs/math/0601042v2

Mathematics

Group Theory

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

Scientific paper

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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