Abstract
Let $G$ be a finite group and $\alpha(G)=\frac{|C(G)|}{|G|}$, where $C(G)$ denotes the set of cyclic subgroups of $G$. In this short note, we prove that $\alpha(G)\leq\alpha(Z(G))$ 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.
Citation
Marius Tărnăuceanu. "A result on the number of cyclic subgroups of a finite group." Proc. Japan Acad. Ser. A Math. Sci. 96 (10) 93 - 94, December 2020. https://doi.org/10.3792/pjaa.96.018
Information