Two-generator subgroups of right-angled Artin groups are quasi-isometrically embedded

2014/12/01 by Mike Carr, Carr, Mike
Mathematics · #20F36 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:20F36

paper · pdf · doi:10.48550/arxiv.1412.0642

21 pages, 13 figures

openalex publication_date 2014/12/01 · arxiv created 2015/10/13 · arxiv updated 2015/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that non-abelian two-generator subgroups of right-angled Artin groups are quasi-isometrically embedded free groups. This provides an alternate proof of a theorem of A. Baudisch: that all two-generator subgroups are free or free abelian. Additionally, it shows that they are quasi-isometrically embedded. Our theorem also gives a method for detecting groups that are not isomorphic to a subgroup of any RAAG. We present some counterexamples in subgroups with more than two generators.

Citations

• Embeddings of right-angled Artin groups

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