Residually finite groups that do not virtually have the unique product property
Group Theory
2026-02-13 v1
Abstract
We construct a finitely generated residually finite group with the property that every finite index subgroup of contains a subgroup isomorphic to Promislow's group. Hence does not have a finite index subgroup with the unique product property.
Keywords
Cite
@article{arxiv.2602.11819,
title = {Residually finite groups that do not virtually have the unique product property},
author = {Naomi Bengi and Daniel T. Wise},
journal= {arXiv preprint arXiv:2602.11819},
year = {2026}
}