A Bound on the Number of Conjugacy Classes of Non-normal Cyclic Subgroups of a Finite p-Group

被引：0
作者：
Hamid Mousavi
Hadi Ahmadi
机构：
[1] University of Tabriz,Department of Mathematical Sciences
来源：
Mediterranean Journal of Mathematics | 2022年 / 19卷
关键词：
Finite ; -groups; non-normal subgroups; conjugacy class of subgroups; Primary 20D15 Secondary 20E45;
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摘要：
Let G be a finite p-group of odd order and let νc(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _c(G)$$\end{document} be the number of conjugacy classes of non-normal cyclic subgroups of G. In this paper, among other results, we obtain a lower bound for νc(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _c(G)$$\end{document}. More precisely, if |G′|=pk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|G'|=p^k$$\end{document}, for some integer k, then we prove that νc(G)≥k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _c(G)\ge k$$\end{document}.
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