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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
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.
Received: 17.01.2020 Revised: 17.01.2020 Accepted: 19.02.2020
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
Linking options:
https://www.mathnet.ru/eng/smj6006 https://www.mathnet.ru/eng/smj/v61/i3/p634
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Abstract page: | 275 | Full-text PDF : | 76 | References: | 44 | First page: | 6 |
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