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15.81 (2002)

Solved

Let $G$ be a finite non-supersoluble group. Is it true that $G$ has a non-cyclic Sylow subgroup $P$ such that some maximal subgroup of $P$ has no proper complement in $G$?

Contributor: A. N. Skiba

Progress

Yes, it is (Wang, Yanming, Wei, Huaquan, Sci. China Ser. A, 47 (2004), no. 1, 96–103).

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