Residually finite groups that do not virtually have the unique product property
Abstract
We construct a finitely generated residually finite group $G$ with the property that every finite index subgroup of $G$ contains a subgroup isomorphic to Promislow's group. Hence $G$ does not have a finite index subgroup with the unique product property.
Fields of Study & Subjects
Geometric and Algebraic Topology
Finite Group Theory Research
Advanced Operator Algebra Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 12 February 2026
- Language
- EN
- Document type
- Preprint