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20.28 (2022)

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Let $L$ be a non-abelian finite simple group, and let $H(L) = M(L).L$ be the universal perfect central extension, where $M(L)$ is the Schur multiplier of $L$. Suppose that $G$ is a finite group such that the set of class sizes of $G$ is the same as the set of class sizes of $H(L)$. Is it true that $G \cong H(L) \times A$, where $A$ is an abelian group?

Contributor: I. B. Gorshkov

Progress

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

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