Simple components and central units in group algebras

Let G be a finite group. Berman [Dokl. Akad. Nauk 106 (1956) 767] and Witt [J. Reine Angew. Math. 190 (1952) 231] evaluate, independently, the number of simple components of the group algebra FG when F is a field of characteristic 0. In this paper we extend this result to fields of arbitrary characteristic which does not divide the order of G. We also compute the rank of the group of the central units of and obtain an alternative proof of a well-known result of Ritter and Sehgal.