We give the characterization of the unit group of FqSL(2, Z₅), where Fq is a finite field with q = pᵏ elements for prime $p > 5,$ and SL(2, Z₅) denotes the special linear group of 2 ×2 matrices having determinant $1$ over the cyclic group Z₅.
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Sharma et al. (2021) studied this question.