Abstract
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.
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Acknowledgments
The authors express gratitude to Alexandre Zalesski for a consultation on the maximal elementary abelian 2-subgroups in orthogonal groups and to Danila Olegovich Revin for providing helpful comments.
Funding
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).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 3, pp. 576–582. https://doi.org/10.33048/smzh.2021.62.309
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Lytkina, D.V., Mazurov, V.D. Locally Finite Periodic Groups Saturated with Finite Simple Orthogonal Groups of Odd Dimension. Sib Math J 62, 462–467 (2021). https://doi.org/10.1134/S0037446621030095
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DOI: https://doi.org/10.1134/S0037446621030095