Relatively Maximal Subgroups of Odd Index in Symmetric Groups

Let 𝖃 be a class of finite groups which contains a group of order 2 and is closed under subgroups, homomorphic images, and extensions. We define the concept of an 𝖃-admissible diagram representing a natural number n. Associated with each n are finitely many such diagrams, and they all can be found e...

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Bibliographic Details
Published inAlgebra and logic Vol. 61; no. 2; pp. 104 - 124
Main Authors Vasil’ev, A. S., Revin, D. O.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.05.2022
Springer
Springer Nature B.V
Subjects
Algebra
Group theory
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
Subgroups
Symmetric functions
Russia
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Summary:Let 𝖃 be a class of finite groups which contains a group of order 2 and is closed under subgroups, homomorphic images, and extensions. We define the concept of an 𝖃-admissible diagram representing a natural number n. Associated with each n are finitely many such diagrams, and they all can be found easily. Admissible diagrams representing a number n are used to uniquely parametrize conjugacy classes of maximal 𝖃-subgroups of odd index in the symmetric group Sym n , and we define the structure of such groups. As a consequence, we obtain a complete classification of submaximal 𝖃-subgroups of odd index in alternating groups.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-022-09680-0