Distortion of embeddings of a torsion-free finitely generated nilpotent group into a unitriangular group

Abstract

In this paper, we study distortion of various well-known embeddings of finitely generated torsion-free nilpotent groups [Formula: see text] into unitriangular groups [Formula: see text]. In particular, we show that there is no undistorted embeddings of [Formula: see text]-dimensional Heisenberg group into [Formula: see text]. We also provide a polynomial time algorithm for finding distortion of a given subgroup of [Formula: see text].