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Locally Finite Periodic Groups Saturated with Finite Simple Orthogonal Groups of Odd Dimension

Authors
  • Lytkina, D. V.1, 2
  • Mazurov, V. D.1
  • 1 Sobolev Institute of Mathematics, Novosibirsk, Russia , Novosibirsk (Russia)
  • 2 Siberian State University of Telecommunications and Information Sciences, Novosibirsk, Russia , Novosibirsk (Russia)
Type
Published Article
Journal
Siberian Mathematical Journal
Publisher
Pleiades Publishing
Publication Date
May 27, 2021
Volume
62
Issue
3
Pages
462–467
Identifiers
DOI: 10.1134/S0037446621030095
Source
Springer Nature
Keywords
License
Yellow

Abstract

Suppose that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ n $\end{document} is an odd integer, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ n\geq 5 $\end{document}. We prove that a periodic group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ G $\end{document}, saturated with finite simple orthogonal groups \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ O_{n}(q) $\end{document} of odd dimension over fields of odd characteristic, is isomorphic to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ O_{n}(F) $\end{document} for some locally finite field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ F $\end{document} of odd characteristic. In particular, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ G $\end{document} is locally finite and countable.

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