Growth of homology torsion of metabelian groups

TL;DR

This paper investigates how torsion in the abelianizations of finite index subgroups in finitely generated metabelian groups grows, extending previous research on finitely presented amenable groups.

Contribution

It provides new insights into torsion growth in metabelian groups, complementing earlier work on finitely presented amenable groups.

Findings

Analyzes torsion growth patterns in metabelian groups

Extends previous results from finitely presented to finitely generated groups

Provides theoretical framework for understanding torsion in abelianizations

Abstract

We study the growth of torsion in the abelianizations of finite index subgroups in finitely generated metabelian groups. This complements earlier work of Kar, Kropholler and the author which covered the finitely presented amenable groups.