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Submaximal Soluble Subgroups of Odd Index in Alternating Groups. / Revin, D. O.

In: Siberian Mathematical Journal, Vol. 62, No. 2, 03.2021, p. 313-323.

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

Harvard

Revin, DO 2021, 'Submaximal Soluble Subgroups of Odd Index in Alternating Groups', Siberian Mathematical Journal, vol. 62, no. 2, pp. 313-323. https://doi.org/10.1134/S0037446621020105

APA

Revin, D. O. (2021). Submaximal Soluble Subgroups of Odd Index in Alternating Groups. Siberian Mathematical Journal, 62(2), 313-323. https://doi.org/10.1134/S0037446621020105

Vancouver

Revin DO. Submaximal Soluble Subgroups of Odd Index in Alternating Groups. Siberian Mathematical Journal. 2021 Mar;62(2):313-323. doi: 10.1134/S0037446621020105

Author

Revin, D. O. / Submaximal Soluble Subgroups of Odd Index in Alternating Groups. In: Siberian Mathematical Journal. 2021 ; Vol. 62, No. 2. pp. 313-323.

BibTeX

@article{17ce90115dee4af1a3befc424fb3bd1f,
title = "Submaximal Soluble Subgroups of Odd Index in Alternating Groups",
abstract = "Let X be a class of finite groups containing a group of even order and closed under subgroups, homomorphic images, and extensions. Then each finite group possesses a maximal X-subgroup of odd index and the study of the subgroups can be reduced to the study of the so-called submaximal X-subgroups of odd index in simple groups. We prove a theorem that deduces the description of submaximal X-subgroups of odd index in an alternating group from the description of maximal X-subgroups of odd index in the corresponding symmetric group. In consequence, we classify the submaximal soluble subgroups of odd index in alternating groups up to conjugacy.",
keywords = "512.542, alternating group, complete class of finite groups, maximal soluble group, soluble group, subgroup of odd index, submaximal soluble group, symmetric group",
author = "Revin, {D. O.}",
note = "Funding Information: The author was supported by the Russian Science Foundation (Grant 19–11–00039). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = mar,
doi = "10.1134/S0037446621020105",
language = "English",
volume = "62",
pages = "313--323",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "2",

}

RIS

TY - JOUR

T1 - Submaximal Soluble Subgroups of Odd Index in Alternating Groups

AU - Revin, D. O.

N1 - Funding Information: The author was supported by the Russian Science Foundation (Grant 19–11–00039). Publisher Copyright: © 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/3

Y1 - 2021/3

N2 - Let X be a class of finite groups containing a group of even order and closed under subgroups, homomorphic images, and extensions. Then each finite group possesses a maximal X-subgroup of odd index and the study of the subgroups can be reduced to the study of the so-called submaximal X-subgroups of odd index in simple groups. We prove a theorem that deduces the description of submaximal X-subgroups of odd index in an alternating group from the description of maximal X-subgroups of odd index in the corresponding symmetric group. In consequence, we classify the submaximal soluble subgroups of odd index in alternating groups up to conjugacy.

AB - Let X be a class of finite groups containing a group of even order and closed under subgroups, homomorphic images, and extensions. Then each finite group possesses a maximal X-subgroup of odd index and the study of the subgroups can be reduced to the study of the so-called submaximal X-subgroups of odd index in simple groups. We prove a theorem that deduces the description of submaximal X-subgroups of odd index in an alternating group from the description of maximal X-subgroups of odd index in the corresponding symmetric group. In consequence, we classify the submaximal soluble subgroups of odd index in alternating groups up to conjugacy.

KW - 512.542

KW - alternating group

KW - complete class of finite groups

KW - maximal soluble group

KW - soluble group

KW - subgroup of odd index

KW - submaximal soluble group

KW - symmetric group

UR - http://www.scopus.com/inward/record.url?scp=85103988295&partnerID=8YFLogxK

U2 - 10.1134/S0037446621020105

DO - 10.1134/S0037446621020105

M3 - Article

AN - SCOPUS:85103988295

VL - 62

SP - 313

EP - 323

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -

ID: 28317997