A note on skew linear groups of finite rank

被引：0
作者：
Le Van Chua
Mai Hoang Bien
Bui Xuan Hai
机构：
[1] University of Science,Faculty of Mathematics and Computer Science
[2] Vietnam National University,undefined
[3] An Giang University,undefined
来源：
Archiv der Mathematik | 2022年 / 119卷
关键词：
Finite rank; Locally solvable group; Skew linear group; Locally finite division ring.; 20E34; 20E25; 20F19; 16K20; 16K40;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The aim of this note is to investigate the structure of skew linear groups of finite rank. Among our results, it is proved that a subgroup G of GLn(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {GL}_n(D)$$\end{document} has finite rank if and only if there exists a solvable normal subgroup N in G of finite rank such that the factor group G/N is finite provided D is a locally finite division ring which is not necessarily commutative.
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页码：113 / 120
页数：7
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