On Olsson's conjecture for blocks with metacyclic defect groups of odd order. (Q543301)

A 1984 conjecture of Olsson 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 of ordinary irreducible characters of height 0 in \(B\) is bounded above by \(|D:D'|\). In the paper under review, the author proves this conjecture in the case that \(D\) is metacyclic. To establish the result, the author can focus on the case that \(p\) is odd, since the even case has been resolved recently by \textit{B. Sambale} [Fusion systems on metacyclic 2-groups. \url{arXiv:0908.0783}].