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14.99 (1999)

Partially Solved

A formation $\mathfrak{F}$ of finite groups is called superradical if it is $S_n$-closed and contains every finite group of the form $G = AB$ where $A$ and $B$ are $\mathfrak{F}$-subnormal $F$-subgroups.
$\qquad$ a) Find all superradical local formations.
$\qquad$ b) Prove that every $S$-closed superradical formation is a solubly saturated formation.

Contributor: L. A. Shemetkov

Progress

b) A counterexample is constructed (S. Yi, S. F. Kamornikov, Siberian Math. J., 57, no. 2 (2016), 260–264).

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