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.