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On commuting elements and embeddings of graph groups and monoids

Part of: Semigroups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  02 February 2009

Mark Kambites
Mark Kambites
Affiliation:
Fachbereich Mathematik/Informatik, Universität Kassel, 34109 Kassel, Germany
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Abstract

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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.

Keywords

graph groupright-angled Artin grouptrace monoidsubgroup

MSC classification

Secondary: 20F36: Braid groups; Artin groups 20M99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 155 - 170
Copyright
Copyright © Edinburgh Mathematical Society 2009