On 2-blocks with \(k(B)-l(B)=1\). (Q258046)

Let \(B\) be a 2-block of a finite group \(G\), let \(k(B)\) be the number of irreducible ordinary characters of \(G\) in \(B\), and let \(l(B)\) be the number of irreducible Brauer characters of \(G\) in \(B\). The author proves that \(k(B)-l(B)=1\) implies that all diagonal entries of the Cartan matrix of \(B\) are even. As a consequence, the author obtains that \(k(B)\neq 3\) for every 2-block \(B\). Reviewer's remark: This last observation also follows from Corollary 1.3 in a paper by \textit{P. Landrock} [J. Algebra 68, 426-442 (1981; Zbl 0452.20007)].