Abelian Splittings and JSJ-Decompositions of Bestvina--Brady Groups

TL;DR

This paper characterizes how Bestvina--Brady groups split over abelian subgroups and provides a detailed JSJ-decomposition, enhancing understanding of their algebraic structure.

Contribution

It introduces a new characterization of splittings over abelian subgroups and constructs a JSJ-decomposition for Bestvina--Brady groups.

Findings

Bestvina--Brady groups split over abelian subgroups under certain conditions

A JSJ-decomposition for Bestvina--Brady groups is constructed

The structural properties of these groups are clarified

Abstract

We give a characterization of Bestvina--Brady groups split over abelian subgroups and describe a JSJ-decomposition of Bestvina--Brady groups.