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On the heritability of the Sylow π-theorem by subgroups. / Vdovin, E. P.; Manzaeva, N. Ch; Revin, D. O.

In: Sbornik Mathematics, Vol. 211, No. 3, 03.2020, p. 309-335.

Research output: Contribution to journal › Article › peer-review

Harvard

Vdovin, EP, Manzaeva, NC & Revin, DO 2020, 'On the heritability of the Sylow π-theorem by subgroups', Sbornik Mathematics, vol. 211, no. 3, pp. 309-335. https://doi.org/10.1070/SM9185

APA

Vdovin, E. P., Manzaeva, N. C., & Revin, D. O. (2020). On the heritability of the Sylow π-theorem by subgroups. Sbornik Mathematics, 211(3), 309-335. https://doi.org/10.1070/SM9185

Vancouver

Vdovin EP, Manzaeva NC, Revin DO. On the heritability of the Sylow π-theorem by subgroups. Sbornik Mathematics. 2020 Mar;211(3):309-335. doi: 10.1070/SM9185

Author

Vdovin, E. P. ; Manzaeva, N. Ch ; Revin, D. O. / On the heritability of the Sylow π-theorem by subgroups. In: Sbornik Mathematics. 2020 ; Vol. 211, No. 3. pp. 309-335.

BibTeX

@article{e51b39117ad74f4dac35094636a1b40e,
title = "On the heritability of the Sylow π-theorem by subgroups",
abstract = "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.",
keywords = "Dπ-group, Finite group, Group of lie type, Maximal subgroup, π-hall subgroup",
author = "Vdovin, {E. P.} and Manzaeva, {N. Ch} and Revin, {D. O.}",
note = "Publisher Copyright: {\textcopyright} 2020 Russian Academy of Sciences (DoM) and London Mathematical Society. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = mar,
doi = "10.1070/SM9185",
language = "English",
volume = "211",
pages = "309--335",
journal = "Sbornik Mathematics",
issn = "1064-5616",
publisher = "Turpion Ltd.",
number = "3",

}

RIS

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