The unit group of some special semi-simple group algebras

Abstract

Let G be a non-abelian group of order 2ⁿ which has a cyclic subgroup of index 2 and let U(F_q[G]) be the unit group of the group algebra F_q[G] of G over the field F_q containing F_q = p^k elements. In this paper, recurrence relations are established to determine the structure of the unit group of F_q[G] when p > 2.

Keywords: Unit group, group algebra, Wedderburn decomposition, Witt-Berman theorem