Metabelianisations of finitely presented groups

TL;DR

This paper investigates whether the maximal metabelian quotients of certain finitely presented groups, including soluble, one-relator, knot, and Artin groups, admit finite presentations, exploring structural properties of these groups.

Contribution

It provides new insights into the finite presentability of maximal metabelian quotients for various classes of finitely presented groups.

Findings

Maximal metabelian quotients of soluble groups may admit finite presentations.

Certain one-relator and knot groups have non-finitely presented metabelian quotients.

Artin groups exhibit diverse behaviors regarding the finite presentability of their metabelian quotients.

Abstract

In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of soluble groups, of one-relator or knot groups, and of Artin groups.