The structure of the unit group of the group algebra $ \mathbb{F}S_{5}$ where $ \mathbb{F} $ is a finite field with $\ch( \mathbb{F})=p>5 $

Abstract: Let $\mathbb{F}_{q}$ denote a field having $q=p^{n}$ elements, where $p$ a prime, and let $S_{5}$ denote the symmetric group of degree $5$. We give a complete structure of the unit group $\mathcal{U}(\mathbb{F}_{q}S_{5})$, $ p>5$.

Keywords: Group algebra, Wedderburn Decomposition, Unit Group

Classification (MSC2000): 16U60

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