9.23 (1984)

Let $G$ be a finite group, $B$ a block of characters of $G$, $D(B)$ its defect group and $k(B)$ (respectively, $k_0(B)$) the number of all irreducible complex characters (of height 0) lying in $B$. Conjectures:
$\qquad$ a) (R. Brauer) $k(B) \leqslant |D(B)|$; this has been proved for $p$-soluble groups (D. Gluck, K. Magaard, U. Riese, P. Schmid, J. Algebra, 279 (2004), 694–719);
$\qquad$ b) (J. B. Olsson) $k_0(B) \leqslant |D(B) : D(B)'|$, where $D(B)'$ is the derived subgroup of $D(B)$;
$\qquad$ c) (R. Brauer) $D(B)$ is abelian if and only if $k_0(B) = k(B)$.