On Brauer's problem 21 (Q1609604)

For a \(p\)-block \(B\) of a finite group \(G\), the authors give a bound of the order of its defect group \(D\) in terms of \(k(B)\), the number of the irreducible ordinary characters in \(B\). The methods used mainly come from \textit{J. Zeng}'s paper [J. Algebra 193, No.~2, 724-727 (1997; Zbl 0886.20008)].