On commuting elements and embeddings of graph groups and monoids

2006/01/03 by Mark Kambites, Kambites, Mark · 1 citation
Computer Science · Mathematics · #20F36 #20M05 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0601042

openalex publication_date 2006/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 free groups. We also obtain corresponding and more general results for monoids.

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