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In this paper, we consider the general linear group GL (2, 7) of 2 2 invertible matrices over the finite field of order 7 and compute the unit group of the semisimple group algebra FqGL (2, 7), where Fq is a finite field. For the computation of the unit group, we need the Wedderburn decomposition of FqGL (2, 7), which is determined by first computing the Wedderburn decomposition of the group algebra Fq (PSL (3, 2) C₂). Here PSL (3, 2) is the projective special linear group of degree 3 over a finite field of 2 elements.
Sivaranjani et al. (Wed,) studied this question.
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