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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 3, Pages 634–640
DOI: https://doi.org/10.33048/smzh.2020.61.311
(Mi smj6006)
 

This article is cited in 2 scientific papers (total in 2 papers)

On the periodic groups saturated with finite simple groups of lie type $b_3$

D. V. Lytkinaab, V. D. Mazurovc

a Siberian State University of Telecommunications and Informatics, Novosibirsk
b Novosibirsk State University
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (458 kB) Citations (2)
References:
Abstract: Let ${\goth M}$ be a set of finite groups. Given a group $G$, denote by ${\goth M}(G)$ the set of all subgroups of $G$ isomorphic to the elements of ${\goth M}$. A group $G$ is said to be saturated with groups from ${\goth M}$ (saturated with ${\goth M}$, for brevity) if each finite subgroup of $G$ lies in an element of ${\goth M}(G)$. We prove that a periodic group $G$ saturated with ${\goth M}=\{O_7(q)\mid q\equiv\pm3(\operatorname{mod} 8)\}$ is isomorphic to $O_7(F)$ for some locally finite field $F$ of odd characteristic.
Keywords: periodic group, group of Lie type, orthogonal group, group saturated with a set of groups.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1613
Russian Science Foundation 19-11-00039
The work of D. V. Lytkina was supported by the Mathematical Center in Akademgorodok under Agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation; the work of V. D. Mazurov was supported by the Russian Science Foundation (Project 19-11-00039).
Received: 17.01.2020
Revised: 17.01.2020
Accepted: 19.02.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 3, Pages 499–503
DOI: https://doi.org/10.1134/S0037446620030118
Bibliographic databases:
Document Type: Article
UDC: 512.44
MSC: 35R30
Language: Russian
Citation: D. V. Lytkina, V. D. Mazurov, “On the periodic groups saturated with finite simple groups of lie type $b_3$”, Sibirsk. Mat. Zh., 61:3 (2020), 634–640; Siberian Math. J., 61:3 (2020), 499–503
Citation in format AMSBIB
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\paper On the periodic groups saturated with finite simple groups of lie type~$b_3$
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\vol 61
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\pages 634--640
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  • This publication is cited in the following 2 articles:
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    Сибирский математический журнал Siberian Mathematical Journal
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