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20.29 (2022)

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Let $S$ be a non-abelian finite simple group. Is it true that for any $n \in \mathbb{N}$, if the set of class sizes of a centreless finite group $G$ is the same as the set of class sizes of the direct power $S^n$, then $G \cong S^n$?

Contributor: I. B. Gorshkov

Progress

This is proved for $S = \text{Alt}_5^2$ in (J. Algebra Appl., 21, no. 11 (2022), Article ID 2250226, 8 p.).

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