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arXiv · 2003.06072

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

Marius Tărnăuceanu
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Abstract

Let $G$ be a finite group and $α(G)=\frac{|C(G)|}{|G|}$\,, where $C(G)$ denotes the set of cyclic subgroups of $G$. In this short note, we prove that $α(G)\leqα(Z(G))$ and we describe the groups $G$ for which the equality occurs. This gives some sufficient conditions for a finite group to be $4$-abelian or abelian.

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Marius Tărnăuceanu. 2020-03-13. A result on the number of cyclic subgroups of a finite group. https://arxiv.org/abs/2003.06072

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