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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2023, Volume 29, Number 4, Pages 140–145
DOI: https://doi.org/10.21538/0134-4889-2023-29-4-140-145 (Mi timm2043) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Examples of Nonpronormal Relatively Maximal Subgroups of Finite Simple Groups

B. Lia, D. O. Revinbc

a Nantong University, School of Science
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
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DOI: https://doi.org/10.21538/0134-4889-2023-29-4-140-145
Abstract: Using R. Wilson's recent results, we prove the existence of triples $(\mathfrak{X},G,H)$ such that $\mathfrak{X}$ is a complete (i.e., closed under taking subgroups, homomorphic images, and extensions) class of finite groups, $G$ is a finite simple group, and $H$ is its $\mathfrak{X}$-maximal subgroup nonpronormal in $G$. This disproves a conjecture stated earlier by the second author and W. Guo.
Keywords: complete class of groups, relatively maximal subgroup, pronormal subgroup, finite simple group.
Funding agency Grant number
National Natural Science Foundation of China 12371021
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0002
The research of B. Li was supported by National Natural Science Foundation of China, (NSFC), grant no.12371021. The research of D. O. Revin was carried out within the State Contract of the Sobolev Institute of Mathematics (FWNF-2022-0002).
Received: 28.08.2023
Revised: 14.09.2023
Accepted: 18.09.2023
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2023, Volume 323, Issue 1, Pages S155–S159
DOI: https://doi.org/10.1134/S0081543823060135
Bibliographic databases:
Document Type: Article
UDC: 517.542
MSC: 20E32 20E28 20D20
Language: Russian
Citation: B. Li, D. O. Revin, “Examples of Nonpronormal Relatively Maximal Subgroups of Finite Simple Groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 29, no. 4, 2023, 140–145; Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S155–S159
Citation in format AMSBIB
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\by B.~Li, D.~O.~Revin
\paper Examples of Nonpronormal Relatively Maximal Subgroups of Finite Simple Groups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2023
\vol 29
\issue 4
\pages 140--145
\mathnet{http://mi.mathnet.ru/timm2043}
\crossref{https://doi.org/10.21538/0134-4889-2023-29-4-140-145}
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\edn{https://elibrary.ru/horvkk}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2023
\vol 323
\issue , suppl. 1
\pages S155--S159
\crossref{https://doi.org/10.1134/S0081543823060135}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85185307147}
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