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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2020 Volume 61, Number 3, Pages 634–640 (Mi smj6006)

This article is cited 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

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.

UDC: 512.44

MSC: 35R30

Received: 17.01.2020
Revised: 17.01.2020
Accepted: 19.02.2020

DOI: 10.33048/smzh.2020.61.311


 English version:
Siberian Mathematical Journal, 2020, 61:3, 499–503

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© Steklov Math. Inst. of RAS, 2025