Author:
Vdovin E. P.,Manzaeva N. Ch.,Revin D. O.
Abstract
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.
Funder
Russian Science Foundation
Subject
Algebra and Number Theory
Cited by
3 articles.
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