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<p>In this paper, we investigate the finiteness properties of subgroups of direct products of 2-dimensional coherent right-angled Artin groups. We explore how these properties relate to the structure of the subgroups and the decidability of certain algorithmic problems. More precisely, we show that a finitely presented subgroup <i>S</i> of the direct product of 2-dimensional coherent RAAGs is virtually a nilpotent extension of a direct product. Moreover, if <i>S</i> is of type <i>FP</i>, then <i>S</i> is commensurable to a kernel of a character. We use these results to show that the multiple conjugacy problem and the membership problem are decidable for finitely presented subgroups of direct products of 2-dimensional coherent RAAGs. This work generalizes the results of Bridson, Howie, Miller, and Short for free groups.</p>

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Finitely presented subgroups of direct products of graphs of groups with free abelian vertex groups

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  • 出版模式：

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  • 发表日期：

    2025年7月8日

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  • Montserrat Casals-Ruiz,
  • Jone Lopez de Gamiz Zearra

摘要

In this paper, we investigate the finiteness properties of subgroups of direct products of 2-dimensional coherent right-angled Artin groups. We explore how these properties relate to the structure of the subgroups and the decidability of certain algorithmic problems. More precisely, we show that a finitely presented subgroup S of the direct product of 2-dimensional coherent RAAGs is virtually a nilpotent extension of a direct product. Moreover, if S is of type FP, then S is commensurable to a kernel of a character. We use these results to show that the multiple conjugacy problem and the membership problem are decidable for finitely presented subgroups of direct products of 2-dimensional coherent RAAGs. This work generalizes the results of Bridson, Howie, Miller, and Short for free groups.