Journal article
On commuting elements and embeddings of graph groups and monoids
Publication Details
Authors: | Kambites, M. |
Publication year: | 2009 |
Journal: | Proceedings of the Edinburgh Mathematical Society |
Pages range : | 155-170 |
Volume number: | 52 |
Start page: | 155 |
End page: | 170 |
ISSN: | 0013-0915 |
Abstract
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 groups. We also obtain corresponding and more. general results in the monoid case.
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 groups. We also obtain corresponding and more. general results in the monoid case.
