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9.73 (1984)

Solved

Let $\mathfrak{F}$ be any local formation of finite soluble groups containing all finite nilpotent groups. Prove that $H^\mathfrak{F} K = K H^\mathfrak{F}$ for any two subnormal subgroups $H$ and $K$ of an arbitrary finite group $G$.

Contributor: L. A. Shemetkov

Progress

This has been proved, even without the hypothesis of solubility of $\mathfrak{F}$ (S. F. Kamornikov, Dokl. Akad. Nauk BSSR, 33, no. 5 (1989), 396–399 (Russian)).

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