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arXiv · 1805.00301

A note on the number of cyclic subgroups of a finite group

Marius Tărnăuceanu·Mihai-Silviu Lazorec
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Abstract

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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Marius Tărnăuceanu, Mihai-Silviu Lazorec. 2018-05-01. A note on the number of cyclic subgroups of a finite group. https://arxiv.org/abs/1805.00301

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