高等级 GBS 群的可分离性

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-13 DOI:10.1112/blms.70024

Jone Lopez de Gamiz Zearra, Sam Shepherd

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引用次数: 0

摘要

秩n$ n$广义Baumslag-Solitar群是一个群分裂为群的有限图，使得所有顶点群和边群同构于Z n$ \mathbb {Z}^n$。在本文中，我们根据它们的可分性对这些群进行分类。具体地说，我们确定了它们何时是剩余有限的，何时是子群可分的，何时是循环子群可分的。

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Separability properties of higher rank GBS groups

A rank $n$ generalized Baumslag–Solitar group is a group that splits as a finite graph of groups such that all vertex and edge groups are isomorphic to $Z^{n}$ . In this paper, we classify these groups in terms of their separability properties. Specifically, we determine when they are residually finite, subgroup separable, and cyclic subgroup separable.