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19.85 (2018)

Solved

Suppose that every Schmidt subgroup of a finite group $G$ is $\sigma$-subnormal in $G$ (see 19.84). Is it true that then there is a normal $\sigma$-nilpotent subgroup $N \leqslant G$ such that $G/N$ is cyclic?

Contributor: A. N. Skiba

Progress

An affirmative answer is known if $\sigma = \{\{2\}, \{3\}, \dots\}$.

Yes, it is true (X. Yi, S. F. Kamornikov, J. Algebra, 560 (2020), 181–191).

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