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Keywords:
unit group; finite field; Wedderburn decomposition
unit group; finite field; Wedderburn decomposition
Summary:
We give the characterization of the unit group of $\mathbb {F}_qSL(2, \mathbb {Z}_5)$, where $\mathbb {F}_q$ is a finite field with $q = p^k$ elements for prime $p > 5,$ and $SL(2, \mathbb {Z}_5)$ denotes the special linear group of $2 \times 2$ matrices having determinant $1$ over the cyclic group $\mathbb {Z}_5$.
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