Regular maps from the lamplighter to metabelian groups
Group Theory
2024-01-17 v1
Abstract
We prove that the lamplighter group admits an injective Lipschitz map to any finitely generated metabelian group which is not virtually nilpotent. This implies that finitely generated metabelian groups satisfy the ``analytically thin/analytically thick'' dichotomy recently introduced by Hume, Mackay and Tessera.
Cite
@article{arxiv.2401.08510,
title = {Regular maps from the lamplighter to metabelian groups},
author = {Antoine Gournay and Corentin Le Coz},
journal= {arXiv preprint arXiv:2401.08510},
year = {2024}
}
Comments
11 pages. Comments are welcome!