关于有限群的循环子群数目的一个结果

M. Tarnauceanu
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引用次数: 1

摘要

设$G$为一个有限群,$L_1(G)$为它的循环子群的偏序集,并考虑量$\alpha(G)=\frac{|L_1(G)|}{|G|}$。本文的目的是研究具有$\alpha(G)=\frac{3}{4}$的有限幂零群$\cal{C}$类。我们证明了如果$G$属于该类,则它是一个满足一定条件的2群。此外,我们还研究了若干类有限群对$\cal{C}$的附属物。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A result on the number of cyclic subgroups of a finite group
Let $G$ be a finite group, $L_1(G)$ be its poset of cyclic subgroups and consider the quantity $\alpha(G)=\frac{|L_1(G)|}{|G|}$. The aim of this paper is to study the class $\cal{C}$ of finite nilpotent groups having $\alpha(G)=\frac{3}{4}$. We show that if $G$ belongs to this class, then it is a 2-group satisfying certain conditions. Also, we study the appartenance of some classes of finite groups to $\cal{C}$.
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