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20.80 (2022)

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Let $G$ be a finite group, and $\chi$ an irreducible complex character of $G$. We call $\chi$ a P-character if $\chi$ is a constituent of $(1_H)^G$ for some maximal subgroup $H$ of $G$; and $\chi$ is said to be monomial if $\chi$ is induced by a linear character of a subgroup of $G$.
Conjecture: $G$ is solvable if and only if all its P-characters are monomial.

Contributor: G. Qian

Progress

The necessity part of the conjecture is true (G. Qian, Y. Yang, Commun. Algebra, 46, no. 1 (2018), 167–175).

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