Separability properties of higher rank GBS groups

Abstract

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.