Субмаксимальные разрешимые подгруппы нечетного индекса в знакопеременных группах

Translated title of the contribution: Submaximal Soluble Subgroups of Odd Index in Alternating Groups

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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.
Translated title of the contributionSubmaximal Soluble Subgroups of Odd Index in Alternating Groups
Original languageRussian
Article number10
Pages (from-to)387–401
Number of pages15
JournalСибирский математический журнал
Volume62
Issue number2
DOIs
Publication statusPublished - Mar 2021

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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