2020/10/20 by Montserrat Casals‐Ruiz, Casals-Ruiz, Montserrat, Jone Lopez de Gamiz Zearra +1
Mathematics · #20E08 (Secondary) #20F65 (Primary) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2010.10414
openalex publication_date 2020/10/20 · openalex created_date 2023/10/04 · openalex updated_date 2026/07/28
A result of Baumslag and Roseblade states that a finitely presented subgroup of the direct product of two free groups is virtually a direct product of free groups. In this paper we generalise this result to the class of cyclic subgroup separable graphs of groups with free abelian vertex groups and cyclic edge groups. More precisely, we show that a finitely presented subgroup of the direct product of two groups in this class is virtually H-by-(free abelian), where H is the direct product of two groups in the class. In particular, our result applies to 2-dimensional coherent right-angled Artin groups and residually finite tubular groups. Furthermore, we show that the multiple conjugacy problem and the membership problem are decidable for finitely presented subgroups of the direct product of two 2-dimensional coherent RAAGs.