Relatively Maximal Subgroups of Odd Index in Symmetric Groups

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Relatively Maximal Subgroups of Odd Index in Symmetric Groups. / Vasil’ev, A. S.; Revin, D. O.

In: Algebra and Logic, Vol. 61, No. 2, 05.2022, p. 104-124.

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

BibTeX

@article{f7ee67d248b344af8f47a125b5109a13,

title = "Relatively Maximal Subgroups of Odd Index in Symmetric Groups",

abstract = "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 Symn, 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.",

keywords = "complete class, maximal x-subgroup, subgroup of odd index, submaximal x-subgroup, symmetric group",

author = "Vasil{\textquoteright}ev, {A. S.} and Revin, {D. O.}",

note = "Funding Information: Supported by Russian Science Foundation, project No. 19-71-10067. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = may,

doi = "10.1007/s10469-022-09680-0",

language = "English",

volume = "61",

pages = "104--124",

journal = "Algebra and Logic",

issn = "0002-5232",

publisher = "Springer US",

number = "2",

}

RIS

TY - JOUR

T1 - Relatively Maximal Subgroups of Odd Index in Symmetric Groups

AU - Vasil’ev, A. S.

AU - Revin, D. O.

PY - 2022/5

Y1 - 2022/5

N2 - 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 Symn, 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.

AB - 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 Symn, 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.

KW - complete class

KW - maximal x-subgroup

KW - subgroup of odd index

KW - submaximal x-subgroup

KW - symmetric group

UR - http://www.scopus.com/inward/record.url?scp=85139818635&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/36ecc51a-3fa5-3b02-95a5-fec31a343ee4/

U2 - 10.1007/s10469-022-09680-0

DO - 10.1007/s10469-022-09680-0

M3 - Article

AN - SCOPUS:85139818635

VL - 61

SP - 104

EP - 124

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 2

ER -

ID: 38184621