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On commuting elements and embeddings of graph groups and monoids
Published online by Cambridge University Press: 02 February 2009
Abstract
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.
MSC classification
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 155 - 170
- Copyright
- Copyright © Edinburgh Mathematical Society 2009
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