Trivial units in commutative group rings of \(G\times C_{n}\)

• Date: 2024
• Main Author: Küsmüş, Ömer
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2024
• Subjects: trivial units; commutative; group rings; direct product; 16S34; 16U60
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2086
• Journal Title: Algebra and Discrete Mathematics

It is known that if the unit group of an integral group ring \(\mathbb{Z}G\) is trivial, then the unit group of \(\mathbb{Z}(G\times C_{2})\) is trivial as well [3]. The aim of this study is twofold: firstly, to identify rings \(R\) that are \(D\)-adapted for the direct product \(D=G\times H\) of ab...