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20.115 (2022)

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Let $\chi$ be a complex irreducible character of a finite group $G$. If $\chi(x) \neq 0$ for some $x \in G$, must the order $o(x)$ of $x$ divide $|G|/\chi(1)$?

This is known to be true if $G$ is solvable, and it is known that $(o(x)\chi(1))^4$ divides $|G|^5$ for arbitrary $G$.

Contributor: T. Wilde

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