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Lytkina, D. V.; Mazurov, V. D.

Locally finite periodic groups saturated with finite simple orthogonal groups of odd dimension. (English. Russian original) Zbl 1506.20075

Sib. Math. J. 62, No. 3, 462-467 (2021); translation from Sib. Mat. Zh. 62, No. 3, 576-582 (2021).
Summary: Suppose that \(n\) is an odd integer, \( n\geq 5 \). We prove that a periodic group \(G \), saturated with finite simple orthogonal groups \(O_n(q)\) of odd dimension over fields of odd characteristic, is isomorphic to \(O_n(F)\) for some locally finite field \(F\) of odd characteristic. In particular, \( G\) is locally finite and countable.

Cited in 1 Document

MSC:

20F50 Periodic groups; locally finite groups

Keywords:

periodic group; group saturated with set of groups; locally finite group; orthogonal group
PDFBibTeX XMLCite
\textit{D. V. Lytkina} and \textit{V. D. Mazurov}, Sib. Math. J. 62, No. 3, 462--467 (2021; Zbl 1506.20075); translation from Sib. Mat. Zh. 62, No. 3, 576--582 (2021)
Full Text: DOI

References:

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