N. Yang, Zh. Wu, D. O. Revin, “On the sharp Baer–Suzuki theorem for the $\pi$-radical: sporadic groups”, Sibirsk. Mat. Zh., 63:2 (2022), 464–472; Siberian Math. J., 63:2 (2022), 387

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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 2, Pages 464–472
DOI: https://doi.org/10.33048/smzh.2022.63.216 (Mi smj7670)

This article is cited in 9 scientific papers (total in 9 papers)

On the sharp Baer–Suzuki theorem for the

π

$\pi$ -radical: sporadic groups

N. Yang^a, Zh. Wu^a, D. O. Revin^bcd

^a Jiangnan University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^c Novosibirsk State University
^d N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Full-text PDF (318 kB) Citations (9)

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DOI: https://doi.org/10.33048/smzh.2022.63.216

Abstract: Let

π

$\pi$ be a proper subset of the set of all primes and

| π | \geq 2

${|\pi|\geq 2}$ . Denote the smallest prime not in

π

$\pi$ by

r

$r$ and let

m = r

$m=r$ if

r = 2, 3

$r=2,3$ , and

m = r - 1

$m=r-1$ if

r \geq 5

$r\geq 5$ . We study the following conjecture: A conjugacy class

D

$D$ of a finite group

G

$G$ lies in the

π

$\pi$ -radical

O_{π} (G)

$\mathrm{O}_\pi(G)$ of

G

$G$ if and only if every

m

$m$ elements of

D

$D$ generate a

π

$\pi$ -subgroup. We confirm this conjecture for the groups

G

$G$ whose every nonabelian composition factor is isomorphic to a sporadic or alternating group.

Keywords: sporadic simple group,

π

$\pi$ -radical of a finite group, Baer–Suzuki

π

$\pi$ -theorem.

Funding agency	Grant number
Russian Science Foundation	19-11-00039
Natural Science Foundation of Jiangsu Province	BK20210442
Jiangsu Shuangchuang, Mass Innovation and Entrepreneurship, Talent Program	JSSCBS20210841
The work was supported by the Russian Science Foundation (GrantВ 19вЂ“11вЂ“00039). Zh.В Wu was supported by the Natural Science Foundation of the Jiangsu Province, China (Grant no.В BK20210442), and the Jiangsu Shuangchuang, Mass Innovation and Entrepreneurship, Talent Program (Grant no.В JSSCBS20210841).

Received: 21.07.2021
Revised: 05.11.2021
Accepted: 10.12.2021

English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 2, Pages 387–394
DOI: https://doi.org/10.1134/S0037446622020161

Document Type: Article

UDC: 512.542

Language: Russian

Citation: N. Yang, Zh. Wu, D. O. Revin, “On the sharp Baer–Suzuki theorem for the

π

$\pi$ -radical: sporadic groups”, Sibirsk. Mat. Zh., 63:2 (2022), 464–472; Siberian Math. J., 63:2 (2022), 387–394

Citation in format AMSBIB

\Bibitem{YanWuRev22}

\by N.~Yang, Zh.~Wu, D.~O.~Revin

\paper On the sharp Baer--Suzuki theorem for the $\pi$-radical: sporadic groups

\jour Sibirsk. Mat. Zh.

\yr 2022

\vol 63

\issue 2

\pages 464--472

\mathnet{http://mi.mathnet.ru/smj7670}

\crossref{https://doi.org/10.33048/smzh.2022.63.216}

\transl

\jour Siberian Math. J.

\yr 2022

\vol 63

\issue 2

\pages 387--394

\crossref{https://doi.org/10.1134/S0037446622020161}

Linking options:

https://www.mathnet.ru/eng/smj7670

https://www.mathnet.ru/eng/smj/v63/i2/p464

This publication is cited in the following 9 articles:

D. O. Revin, “Shirina Bera–Suzuki polnogo klassa konechnykh grupp konechna”, Algebra i analiz, 37:1 (2025), 141–176
D. O. Revin, A. V. Zavarnitsine, “Generation by conjugate elements of finite almost simple groups with a sporadic socle”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 49 (2024), 135–142
A-M. Liu, Zh. Wang, D. O. Revin, “Toward a Sharp Baer–Suzuki Theorem for the π-Radical: Unipotent Elements of Groups of Lie Type”, Algebra Logic, 2024
N. Yang, Zh. Wu, D. O. Revin, E. P. Vdovin, “On the sharp Baer-Suzuki theorem for the $\pi$ -radical of a finite group”, Sb. Math., 214:1 (2023), 108–147
Ch. Van, V. Go, D. O. Revin, “K tochnoi teoreme Bera–Suzuki dlya $\pi$ -radikala: isklyuchitelnye gruppy malogo ranga”, Algebra i logika, 62:1 (2023), 3–32
Danila O. Revin, Andrei V. Zavarnitsine, “On generations by conjugate elements in almost simple groups with socle 2𝐹4(𝑞2)′”, Journal of Group Theory, 2023
Zh. Wang, W. Guo, D. O. Revin, “Toward a Sharp Baer–Suzuki Theorem for the π-Radical: Exceptional Groups of Small Rank”, Algebra Logic, 62:1 (2023), 1
A.-M. Lyu, Ch. Van, D. O. Revin, “K tochnoi teoreme Bera–Suzuki dlya $\pi$ -radikala: unipotentnye elementy grupp lieva tipa”, Algebra i logika, 62:6 (2023), 708–741
J. Guo, W. Guo, D. O. Revin, V. N. Tyutyanov, “On the Baer–Suzuki Width of Some Radical Classes”, Proc. Steklov Inst. Math. (Suppl.), 317, suppl. 1 (2022), S90–S97

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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