Metabelian groups with quadratic Dehn function and Baumslag-Solitar groups

TL;DR

This paper demonstrates that a specific class of metabelian locally compact groups have quadratic Dehn functions and shows how Baumslag-Solitar groups can be embedded into finitely presented metabelian groups with this property.

Contribution

It establishes quadratic Dehn functions for certain metabelian groups and provides new embeddings of Baumslag-Solitar groups into finitely presented metabelian groups.

Findings

Metabelian groups in the studied class have quadratic Dehn functions.

Baumslag-Solitar groups can be embedded into finitely presented metabelian groups with quadratic Dehn functions.

Finitely presented metabelian groups containing lamplighter groups also have quadratic Dehn functions.

Abstract

We prove that groups in a certain class of metabelian locally compact groups, have quadratic Dehn function. As an application, we embed the solvable Baumslag-Solitar groups into finitely presented metabelian groups with quadratic Dehn function. Also, we prove that Baumslag's finitely presented metabelian groups, in which the lamplighter groups embed, have quadratic Dehn function.