On the number of maximal subgroups of a finite solvable group

被引:0
|
作者
Benjamin Newton
机构
[1] Beloit College,
来源
Archiv der Mathematik | 2011年 / 96卷
关键词
20E28; 20D10; Maximal subgroups; Solvable groups;
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摘要
For a finite solvable group G and prime number p, we use elementary methods to obtain an upper bound for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {m}_{p}(G)}$$\end{document} , defined as the number of maximal subgroups of G whose index in G is a power of p. From this we derive an upper bound on the total number of maximal subgroups of a finite solvable group in terms of its order. This bound improves existing bounds, and we identify conditions on the order of a finite solvable group under which this bound is best possible.
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页码:501 / 506
页数:5
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