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Submaximal Soluble Subgroups of Odd Index in Alternating Groups. / Revin, D. O.
в: Siberian Mathematical Journal, Том 62, № 2, 03.2021, стр. 313-323.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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