Unit Group of the Group Algebra F_qGL(2,7) - Sivaranjani, Namatchivayam Umapathy; Nandakumar, Elumalai; Mittal, Gaurav; Sharma, Rajendra Kumar (Armenian Journal of Mathematics, 2024)
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 F_qGL(2,7), where F_q is a finite field. For the computation of the unit group, we need the Wedderburn decomposition of F_qGL(2,7), which is determined by first computing the Wedderburn decomposition of the group algebra F_q(PSL(3, 2) times C_2). Here PSL(3,2) is the projective special linear group of degree 3 over a finite field of 2 elements.