Undistorted embeddings of metabelian groups of finite Pr\"ufer rank

TL;DR

This paper investigates how metabelian groups of finite Prüfer rank can be embedded into constructible groups, focusing on the metric distortions of these embeddings.

Contribution

It provides a detailed analysis of the metric distortions in embeddings of metabelian groups of finite Prüfer rank into constructible groups.

Findings

Analysis of metric distortions in specific embeddings

Identification of conditions affecting distortion levels

Insights into embedding behavior of metabelian groups

Abstract

General arguments of Baumslag and Bieri guarantee that any metabelian group of finite Pr\"ufer rank can be embedded in a metabelian constructible group. Here, we consider the metric behavior of a rich class of examples and analyze the distortions of specific embeddings.