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6.52 (1978)

Solved

Let $f$ be a local screen of a formation which contains all finite nilpotent groups and let $A$ be a group of automorphisms of a finite group $G$. Suppose that $A$ acts $f$-stably on the socle of $G/\Phi(G)$. Is it true that $A$ acts $f$-stably on $\Phi(G)$?

Contributor: L. A. Shemetkov

Progress

No, not always (A. N. Skiba, Siber. Math. J., 34 (1993), 953–958).

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