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6.42 (1978)

Solved

Let $H$ be a strongly 3-embedded subgroup of a finite group $G$. Suppose that $Z(H/O_{3'}(H))$ contains an element of order 3. Does $Z(G/O_{3'}(G))$ necessarily contain an element of order 3?

Contributor: N. D. Podufalov

Progress

Yes, it does (mod CFSG) (W. Xiao, Sci. China (A), 33 (1990), 1172–1181).

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