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4.22 (1973)

Solved

(J. G. Thompson). Let $G$ be a finite group, $A$ a group of automorphisms of $G$ such that $|A|$ and $|G|$ are coprime. Does there exist an $A$-invariant soluble subgroup $H$ of $G$ such that $C_A(H) = 1$?

Contributor: G. Glauberman

Progress

Yes, it does (S. A. Syskin, Siberian Math. J., 32, no. 6 (1991), 1034–1037).

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