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13.43 (1995)

Open

(G. R. Robinson). Let $G$ be a finite group and $B$ be a $p$-block of characters of $G$. Conjecture: If the defect group $D = D(B)$ of the block $B$ is non-abelian, and if $|D : Z(D)| = p^a$, then each character in $B$ has height strictly less than $a$.

Contributor: J. Olsson

Progress

G. R. Robinson's comment of 2020: the conjecture is proved mod CFSG for $p \neq 2$ in (Z. Feng, C. Li, Y. Liu, G. Malle, J. Zhang, Compos. Math., 155, no. 6 (2019), 1098–1117).

Editors' comment: The conjecture is proved (R. Kessar, G. Malle, J. London Math. Soc. (2), 111, no. 2 (2025), Article ID e70076, https://arxiv.org/abs/2311.13510).

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