论文标题
带有自由Abelian顶点组的组图的直接乘积亚组
Subgroups of the direct product of graphs of groups with free abelian vertex groups
论文作者
论文摘要
Baumslag和Roseblade的结果指出，两个自由组的直接乘积有限的亚组实际上是免费组的直接产物。在本文中，我们将此结果推广到具有游离Abelian顶点组和环状边缘组的组的循环亚组类别的类别。更确切地说，我们表明，该课程中两个组的直接产品有限呈现的子组几乎是$ h $ by-（免费的abelian），其中$ h $是同类中两个组的直接产品。特别是，我们的结果适用于二维相干右角artin组和残留有限的管状基团。此外，我们表明，多重共轭问题和成员资格问题对于有限呈现的两个$ 2 $维二维相干RAAG的直接乘积的亚组是可决定的。
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.
