Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
On the heritability of the Sylow π-theorem by subgroups. / Vdovin, E. P.; Manzaeva, N. Ch; Revin, D. O.
в: Sbornik Mathematics, Том 211, № 3, 03.2020, стр. 309-335.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - On the heritability of the Sylow π-theorem by subgroups
AU - Vdovin, E. P.
AU - Manzaeva, N. Ch
AU - Revin, D. O.
N1 - Publisher Copyright: © 2020 Russian Academy of Sciences (DoM) and London Mathematical Society. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/3
Y1 - 2020/3
N2 - Let π be a set of primes. We say that the Sylow π-theorem holds for a finite group G, or G is a Dπ-group, if the maximal π-subgroups of G are conjugate. Obviously, the Sylow π-theorem implies the existence of π-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 Dπ-group an overgroup of a π-Hall subgroup is always a Dπ-group.
AB - Let π be a set of primes. We say that the Sylow π-theorem holds for a finite group G, or G is a Dπ-group, if the maximal π-subgroups of G are conjugate. Obviously, the Sylow π-theorem implies the existence of π-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 Dπ-group an overgroup of a π-Hall subgroup is always a Dπ-group.
KW - Dπ-group
KW - Finite group
KW - Group of lie type
KW - Maximal subgroup
KW - π-hall subgroup
UR - http://www.scopus.com/inward/record.url?scp=85087454560&partnerID=8YFLogxK
U2 - 10.1070/SM9185
DO - 10.1070/SM9185
M3 - Article
VL - 211
SP - 309
EP - 335
JO - Sbornik Mathematics
JF - Sbornik Mathematics
SN - 1064-5616
IS - 3
ER -
ID: 24444742