The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$

• Date: 2024
• Main Authors: Sharma, R. K., Kumar, Yogesh, Mishra, D. C.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2024
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7500
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 512.5 Let $p$ be a prime, $\mathbb{F}_q$ be a finite field with $q=p^n$ elements, and $\mathbb{Z}_9\rtimes\mathbb{Z}_3$ be the  semidirect product of the groups  $\mathbb{Z}_9 $ and $\mathbb{Z}_3$. The unit group $\mathcal{U}(\mathbb{F}_q(\mathbb{Z}_9\rtime...