A sufficient condition for finite presentability of abelian-by-nilpotent groups

TL;DR

This paper provides a geometric method to determine when abelian-by-nilpotent groups are finitely presented, extending previous work on metabelian groups to a broader class.

Contribution

It introduces a generalized geometric construction that offers a sufficient condition for finite presentability of abelian-by-nilpotent groups, building on earlier methods for metabelian groups.

Findings

Provides a new geometric recipe for finite presentability

Extends Bieri and Strebel's construction to abelian-by-nilpotent groups

Offers criteria to identify finitely presented groups in this class

Abstract

A recipe for obtaining finitely presented abelian-by-nilpotent groups is given. It relies on a geometric procedure that generalizes the construction of finitely presented metabelian groups introduced by R. Bieri and R. Strebel in 1980.