Residually finite groups with uniformly almost flat quotients
Group Theory
2025-09-25 v3 Combinatorics
Abstract
We show that if all the finite coset spaces of a polycyclic group have diameter bounded uniformly below by a polynomial in their size then the group is virtually nilpotent. We obtain the same conclusion for a finitely generated residually torsion-free nilpotent group under the weaker assumption that the finite quotient groups have diameter bounded uniformly below by a polynomial in their size. This extends work of Khukhro and Valette.
Cite
@article{arxiv.2410.23035,
title = {Residually finite groups with uniformly almost flat quotients},
author = {David Guo and Matthew Tointon},
journal= {arXiv preprint arXiv:2410.23035},
year = {2025}
}
Comments
36 pages, minor edits and corrections compared to V1 and V2. Accepted for publication in Advances in Mathematics