2023/10/09 by Montserrat Casals‐Ruiz, Casals-Ruiz, Montserrat, Jone Lopez de Gamiz Zearra +1
Mathematics · #20E08 (Secondary) #20F65 (Primary) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2310.05795
openalex publication_date 2023/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A result by Bridson, Howie, Miller, and Short states that if S is a finitely presented subgroup of the direct product of free groups, then S is virtually a nilpotent extension of a direct product of free groups. Moreover, if S is a subgroup of type FPn of the direct product of n free groups, then the nilpotent extension is finite, so S is actually virtually the direct product of free groups. In this paper, these results are generalized to 2-dimensional coherent right-angled Artin groups. More precisely, we show that a finitely presented subgroup of the direct product of 2-dimensional coherent RAAGs is still virtually a nilpotent extension of a direct product of subgroups. If S is moreover a type FPn subgroup of the direct product of n 2-dimensional coherent RAAGs, then S is commensurable to a kernel of a character of a direct product of subgroups. Finally, we show that the multiple conjugacy problem and the membership problem are decidable for finitely presented subgroups of direct products of 2-dimensional coherent RAAGs.