Abstract
Let be a set of primes. We say that the Sylow -theorem holds for a finite group , or is a -group, if the maximal -subgroups of are conjugate. Obviously, the Sylow -theorem implies the existence of -Hall subgroups. In this paper, we give an affirmative answer to Problem 17.44, (b), in the Kourovka notebook: namely, we prove that in a -group an overgroup of a -Hall subgroup is always a -group. Bibliography: 52 titles.
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