Isomorphism classification of Leary-Minasyan groups

TL;DR

This paper classifies the isomorphism types of Leary-Minasyan groups, a class of groups including Baumslag-Solitar groups, based on their algebraic and geometric properties.

Contribution

It provides a complete isomorphism classification of the groups G(A,L), extending understanding of their structure and properties.

Findings

Classification of G(A,L) groups up to isomorphism

Identification of properties like CAT(0) and biautomaticity within the class

Connections to known groups such as Baumslag-Solitar groups

Abstract

Recently, I. J. Leary and A. Minasyan studied the class of groups $G(A,L)$ defined as commensurating HNN-extensions of $\mathbb{Z}^n$. This class, containing the class of Baumslag-Solitar groups, also includes other groups with curious properties, such as being CAT(0) but not biautomatic. In this paper, we classify the groups $G(A,L)$ up to isomorphism.