On block induction. III (Q1337445)

It is described how the Brauer map connects the radicals of the centers of the group algebras of a finite group and a normal subgroup. This is done by extending some results in the second paper in this series [ibid. 159, 477-487 (1993; Zbl 0807.20012)]. It is shown that in certain cases the \(p\)-regular induction defined in that paper is equivalent to the notion of extended block induction as defined by \textit{W. Wheeler} [J. Lond. Math. Soc., II. Ser. 49, 73-82 (1994; Zbl 0799.20011)].