On Gardam's and Murray's units in group rings

• Date: 2023
• Main Author: Bartholdi, L.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: Kaplansky conjecture; units in group rings; 20C07; 16S34
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2053
• Journal Title: Algebra and Discrete Mathematics

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.