Periodic Groups Saturated with Finite Simple Unitary Groups of Degree 4 over Finite Fields of Odd Characteristic

被引：0

作者：

Ma, X. J. ^{[1
]}

Mao, Y. M. ^{[1
]}

Lytkina, D. V. ^{[2
,3
]}

Mazurov, V. D. ^{[2
,4
]}

机构：

[1] Shanxi Datong Univ, Sch Math & Stat, Datong, Peoples R China

[2] Siberian State Univ Telecommun & Informat Sci, Novosibirsk, Russia

[3] Novosibirsk State Univ, Novosibirsk, Russia

[4] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2024年 / 65卷 / 05期

基金：

中国国家自然科学基金;

关键词：

periodic group; locally finite group; involution; centralizer; saturation; unitary group; 512.542;

D O I：

10.1134/S003744662405015X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ M $\end{document} is some nonempty set of finite groups. A group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ G $\end{document} is saturated with groups from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ M $\end{document} if each finite subgroup of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ G $\end{document} lies in a subgroup isomorphic to an element of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ M $\end{document}. We prove that a periodic group with locally finite centralizers of involutions which is saturated with simple unitary groups of degree 4 over finite fields of fixed odd characteristic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ p $\end{document} is isomorphic to a simple unitary group of degree 4 over some locally finite field of characteristic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ p $\end{document}.

引用

页码：1165 / 1169

页数：5

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