Abelian JSJ decomposition of graphs of free abelian groups

TL;DR

This paper constructs an explicit, computable JSJ decomposition for vGBS groups, which are groups decomposable into finite graphs of free abelian groups, enhancing understanding of their structure.

Contribution

The paper provides a method to explicitly compute the JSJ decomposition of vGBS groups over abelian groups, with local modifications to initial graphs.

Findings

JSJ decomposition for vGBS groups is explicitly computable

Decomposition can be obtained by local changes on initial graphs

Enhances understanding of free abelian group structures

Abstract

A group G is a vGBS group if it admits a decomposition as a finite graph of groups with all edge and vertex groups finitely generated and free abelian. We construct the JSJ decomposition of a vGBS group over abelian groups. We prove that this decomposition is explicitly computable, and may be obtained by local changes on the initial graph of groups.