The unit group of some special semi-simple group algebras

Unit Group of the Group Algebra $\mathbb{F}_qGL(2,7)$

“…In addition to this, the recent counterexample to the renowned Kaplansky's unit conjecture further emphasizes the need of research in this area (see [11]). It has been extensively investigated how the unit group of the group algebra F q G is structured (see [1,3,4,[16][17][18]20,21,23,25,27,28]). Furthermore, there have been significant developments in the exploration of the unit group of modular group algebras, in addition to integral and semisimple group algebras (see [5][6][7][8] and the references therein for a comprehensive and recent literature in this direction).…”

Units in $F(C_n \times Q_{12})$ and $F(C_n \times D_{12})$

“…Certain properties of the group of normalized units of the modular group algebras of these groups were studied in [1,2]. Moreover, the structures of the semisimple group algebras of these groups have been obtained in [17,21].…”

“…The groups D 2n , n ≥ 3 and Q 4n , n ≥ 2 also contain a normal cyclic subgroup of index 2 and the unit groups of the group algebras of these groups and their extensions have been extensively studied [6,7,9,11,13,14,16,17,18,21,23,25,26]. In this paper, we aim to contribute in this direction further by describing the structures…”

Unit group of $\f_{p^k}\SL(3,2),p\geq 11$

“…Howerver the complexity of the problem increases with increase in the size of the group and the number of conjugacy classes it has. For more, one can check [MSS2], [MA], [TG] et cetera.…”