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19.30 (2018)

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An element $g$ of a finite group $G$ is said to be vanishing if $\chi(g) = 0$ for some ordinary irreducible complex character $\chi \in \text{Irr}(G)$. Must a finite group and a finite simple group be isomorphic if they have equal orders and the same set of orders of vanishing elements?

Contributor: M. Foroudi Ghasemabadi, A. Iranmanesh

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