Structure of Some Classes of Semisimple Group Algebras Over Finite Fields

Abstract

Abstract. In continuation to the investigation initiated by Ferraz, Goodaire and Milies in [4], we provide an explicit description for the Wedderburn decomposition of finite semisimple group algebras of the class of finite groups G, such that G/Z(G) ∼ = C 2 × C 2 , where Z(G) denotes the center of G.

Finite semisimple group algebra of a normally monomial group

“…Let F q denote the field containing q elements and let G be a finite group of order relatively prime to q, so that the group algebra F q G is semisimple. The knowledge of the algebraic structure of F q G has applications in coding theory and is useful in describing the automorphism group as well as the unit group of F q G. This has attracted the attention of several authors [1,2,3,8,9,11,17,18,22].…”