On Brauer's \(k(B)\)-problem for blocks with metacyclic defect groups of odd order.
A famous conjecture in the modular representation theory of finite groups is Brauer's \(k(B)\)-problem which states that if \(G\) is a finite group, \(p\) a prime and \(B\) a \(p\)-block of \(G\) with defect group \(D\), then the number \(k(B)\) of ordinary irreducible characters in \(B\) is bounded above by \(|D|\). In the paper under review, the conjecture is proved under the additional hypothesis that \(D\) is metacyclic and \(p\) is odd.
scientific article; zbMATH DE number 5956235
scientific article