A note on the number of irreducible characters in a p-block with normal defect group
In a previous paper [Osaka J. Math. 21, 387-398 (1984; Zbl 0538.20007)] the author had proved that for a finite p-solvable group the number of irreducible characters in a p-block is bounded by the order of its defect group D provided that p is large compared with the sectional rank of D, a special case of Brauer's conjecture. In this short note he applies this to prove the analogous result for blocks with normal defect group in an arbitrary finite group. The proof could have been even shorter by referring to a result of \textit{W. F. Reynolds} on the structure of blocks with normal defect groups [Nagoya Math. J. 22, 15-32 (1963; Zbl 0131.263)].
scientific article; zbMATH DE number 3865547