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graph group

Proceedings of the Edinburgh Mathematical Society (1)

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On commuting elements and embeddings of graph groups and monoids
Part of
- Special aspects of infinite or finite groups
- Semigroups
Mark Kambites
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 1 / February 2009

Published online by Cambridge University Press:

02 February 2009, pp. 155-170
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We study commutation properties of subsets of right-angled Artin groups and trace monoids. We show that if Γ is any graph not containing a four-cycle without chords, then the group G(Γ) does not contain four elements whose commutation graph is a four-cycle; a consequence is that G(Γ) does not have a subgroup isomorphic to a direct product of non-abelian groups. We also obtain corresponding and more general results in the monoid case.