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

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 $\mathcal{C}$ 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 $\mathcal{C}$.

arXiv comment13 pages

References in corpus (3)

• Embedding Properties in Central Products
• On some probabilistic aspects of (generalized) dicyclic groups
• An affirmative answer to the Jainkin-Zapirain's question

Cited by in corpus (1)

• The second minimum/maximum value of the number of cyclic subgroups of finite $p$-groups