On the number of irreducible characters in a finite group. II (Q1061835)

[Part I, cf. ibid. 12, 74-82 (1983; Zbl 0517.20002).] Let B be a p-block of the finite group G, P a Sylow p-subgroup of G, D a defect group of B, k(B) the number of irreducible complex characters in B and m(B) the number of indecomposable direct summands of the block ideal B considered as a P-module under the conjugation action. The main result of this paper asserts that \(| P:D| k(B)\leq m(B)\) if D is contained in the center of P. Furthermore, the author corrects an error occurring in his earlier paper [ibid. 10, 319-332 (1981; Zbl 0471.20004)].