On Gardam's and Murray's units in group rings
We show that the units found in torsion-free group rings by Gardam are twisted unitary elements. This justifies some choices in Gardam's construction that might have appeared arbitrary, and yields more examples of units. We note that all units found up to date exhibit non-trivial symmetry.
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| Date: | 2023 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2023
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2053 |
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| Journal Title: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-20532023-06-19T05:16:02Z On Gardam's and Murray's units in group rings Bartholdi, L. Kaplansky conjecture, units in group rings 20C07, 16S34 We show that the units found in torsion-free group rings by Gardam are twisted unitary elements. This justifies some choices in Gardam's construction that might have appeared arbitrary, and yields more examples of units. We note that all units found up to date exhibit non-trivial symmetry. Lugansk National Taras Shevchenko University 2023-06-18 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2053 10.12958/adm2053 Algebra and Discrete Mathematics; Vol 35, No 1 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2053/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2053/1060 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2053/1061 Copyright (c) 2023 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2023-06-19T05:16:02Z |
| collection |
OJS |
| language |
English |
| topic |
Kaplansky conjecture units in group rings 20C07 16S34 |
| spellingShingle |
Kaplansky conjecture units in group rings 20C07 16S34 Bartholdi, L. On Gardam's and Murray's units in group rings |
| topic_facet |
Kaplansky conjecture units in group rings 20C07 16S34 |
| format |
Article |
| author |
Bartholdi, L. |
| author_facet |
Bartholdi, L. |
| author_sort |
Bartholdi, L. |
| title |
On Gardam's and Murray's units in group rings |
| title_short |
On Gardam's and Murray's units in group rings |
| title_full |
On Gardam's and Murray's units in group rings |
| title_fullStr |
On Gardam's and Murray's units in group rings |
| title_full_unstemmed |
On Gardam's and Murray's units in group rings |
| title_sort |
on gardam's and murray's units in group rings |
| description |
We show that the units found in torsion-free group rings by Gardam are twisted unitary elements. This justifies some choices in Gardam's construction that might have appeared arbitrary, and yields more examples of units. We note that all units found up to date exhibit non-trivial symmetry. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2053 |
| work_keys_str_mv |
AT bartholdil ongardamsandmurraysunitsingrouprings |
| first_indexed |
2025-12-02T15:50:07Z |
| last_indexed |
2025-12-02T15:50:07Z |
| _version_ |
1850412218275856384 |