Characterization of finite p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{p}$$\end{document}-groups by their Schur multiplier

被引：0
作者：
Sumana Hatui
机构：
[1] Harish-Chandra Research Institute,School of Mathematics
[2] Homi Bhabha National Institute,undefined
来源：
Proceedings - Mathematical Sciences | 2018年 / 128卷 / 4期
关键词：
Schur multiplier; finite ; -groups; 20D15; 20E34;
D O I：
10.1007/s12044-018-0419-y
中图分类号：
学科分类号：
摘要：
Let G be a finite p-group of order pn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^n$$\end{document} and M(G) be its Schur multiplier. It is a well known result by Green that |M(G)|=p12n(n-1)-t(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|M(G)|= p^{\frac{1}{2}n(n-1)-t(G)}$$\end{document} for some t(G)≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t(G) \ge 0$$\end{document}. In this article, we classify non-abelian p-groups G of order pn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^n$$\end{document} for t(G)=logp(|G|)+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t(G)=\log _p(|G|)+1$$\end{document}.
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