In this paper, we characterize the unit groups of semisimple group algebras $\mathbb{F}_qG$ of non-metabelian groups of order $108$, where $F_q$ is a field with $q=p^k$ elements for some prime $p > 3$ and positive integer $k$. Up to isomorphism, there are $45$ groups of order $108$ but only $4$ of them are non-metabelian. We consider all the non-metabelian groups of order $108$ and find the Wedderburn decomposition of their semisimple group algebras. And as a by-product obtain the unit groups.
Birincil Dil | İngilizce |
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Konular | Mühendislik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 20 Mayıs 2021 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 8 Sayı: 2 |