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14.62 (1999)

Solved

Suppose that $H$ is a non-soluble normal subgroup of a finite group $G$. Does there always exist a maximal soluble subgroup $S$ of $H$ such that $G = H \cdot N_G(S)$?

Contributor: V. S. Monakhov

Progress

Yes, it always exists mod CFSG (V. I. Zenkov, V. S. Monakhov, D. O. Revin, Algebra and Logic, 43, no. 2 (2004), 102–108).

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