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19.33 (2018)

Open

Conjecture: Let $G$ be a finite group, $p$ a prime number, and $P$ a Sylow $p$-subgroup of $G$. Suppose that an irreducible ordinary character $\chi$ of $G$ has degree divisible by $p$. If the restriction $\chi_P$ of $\chi$ to $P$ has a linear constituent, then $\chi_P$ has at least $p$ different linear constituents.

Contributor: E. Giannelli

Progress

This conjecture has been verified for symmetric, alternating, $p$-solvable, and sporadic simple groups.

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