New examples of torsion-free non-unique product groups

Author:

Carter William

Abstract

Abstract.We give an infinite family of torsion-free groups that do not satisfy the unique product property. For these examples, we also show that each group contains arbitrarily large sets whose square has no uniquely represented element.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Units, zero-divisors and idempotents in rings graded by torsion-free groups;Journal of Group Theory;2024-01-25

2. Formalizing Giles Gardam’s Disproof of Kaplansky’s Unit Conjecture;Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs;2024-01-09

3. Small sets without unique products in torsion-free groups;Journal of Algebra and Its Applications;2023-10-06

4. Rips construction without unique product;Pacific Journal of Mathematics;2023-05-03

5. A counterexample to the unit conjecture for group rings;Annals of Mathematics;2021-11-01

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