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12.74 (1992)

Solved

Let $\mathfrak{F}$ be a non-primary one-generator composition formation of finite groups. Is it true that if $\mathfrak{F} = \mathfrak{M}\mathfrak{H}$ and the formations $\mathfrak{M}$ and $\mathfrak{H}$ are non-trivial, then $\mathfrak{M}$ is a composition formation?

Contributor: A. N. Skiba

Progress

This is true if $\mathfrak{F} \neq \mathfrak{H}$ (A. N. Skiba, Algebra of formations, Belaruskaja Navuka, Minsk, 1997, p. 144 (Russian)). In general the answer is negative (W. Guo, Commun. Algebra, 28, no. 10 (2000), 4767–4782).

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