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8.51 (1982)

Open

(J. McKay). If $G$ is a finite group and $p$ a prime let $m_p(G)$ denote the number of ordinary irreducible characters of $G$ whose degree is not divisible by $p$. Let $P$ be a Sylow $p$-subgroup of $G$. Is it true that $m_p(G) = m_p(N_G(P))$?

Contributor: J. B. Olsson

Progress

Yes, it is true (M. Cabanes, B. Späth, Preprint, 2024, https://arxiv.org/abs/2410.20392).

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