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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2603.22640 |
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| _version_ | 1866918407368081408 |
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| author | Dietrich, Heiko Lee, Melissa Nies, Andre Vinyals, Marc |
| author_facet | Dietrich, Heiko Lee, Melissa Nies, Andre Vinyals, Marc |
| contents | We report on some computational experiments related to the trivial units property and unique product property for group rings of torsion-free groups. These properties are related to Kaplansky's unit and zero-divisor conjectures. Our investigations include a classification of certain symmetric non-trivial units in the binary group ring of the Hantzsche-Wendt group; this group was used in Gardam's refutal of Kaplansky's unit conjecture. We also exhibit and investigate a new candidate group that fails the unique units property but may satisfy the trivial unit property. No examples of groups with these properties are known to date. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22640 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the trivial units property and the unique product property Dietrich, Heiko Lee, Melissa Nies, Andre Vinyals, Marc Group Theory We report on some computational experiments related to the trivial units property and unique product property for group rings of torsion-free groups. These properties are related to Kaplansky's unit and zero-divisor conjectures. Our investigations include a classification of certain symmetric non-trivial units in the binary group ring of the Hantzsche-Wendt group; this group was used in Gardam's refutal of Kaplansky's unit conjecture. We also exhibit and investigate a new candidate group that fails the unique units property but may satisfy the trivial unit property. No examples of groups with these properties are known to date. |
| title | On the trivial units property and the unique product property |
| topic | Group Theory |
| url | https://arxiv.org/abs/2603.22640 |