On permutable subgroups of finite groups

被引:2
|
作者
M. Asaad
A. A. Heliel
机构
[1] Cairo University,
[2] Faculty of Science,undefined
[3] Department of Mathematics,undefined
[4] Giza 12613,undefined
[5] Egypt,undefined
[6] e-mail: moasmohs@frcu.eun.eg,undefined
来源
Archiv der Mathematik | 2003年 / 80卷
关键词
Mathematics Subject Classification (1991): 20D10, 20D30.;
D O I
暂无
中图分类号
学科分类号
摘要
Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \frak Z $\end{document} be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \frak Z $\end{document} contains exactly one and only one Sylow p-subgroup of G. A subgroup H of a finite group G is said to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \frak Z $\end{document}-permutable if H permutes with every member of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \frak Z $\end{document}. The purpose here is to study the influence of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \frak Z $\end{document}-permutability of some subgroups on the structure of finite groups. Some recent results are generalized.
引用
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页码:113 / 118
页数:5
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