Metric properties and distortion in some nilpotent groups of matrices

TL;DR

This paper computes metric estimates for certain nilpotent matrix groups and uses these to analyze the distortion of various embeddings between these groups.

Contribution

It provides new metric estimates for nilpotent groups of matrices and applies them to determine distortion functions of group embeddings.

Findings

Metric estimates for specific nilpotent groups are established.

Distortion functions of embeddings between these groups are computed.

The results improve understanding of geometric properties of nilpotent matrix groups.

Abstract

Metric estimates are quantities that approximate the word metric of a finitely presented group up to multiplicative constants. In this paper, they are computed for some nilpotent groups and used to compute the distortion functions of several embeddings between them.