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

Mihai-Silviu Lazorec, Rulin Shen, Marius Tărnăuceanu

Let $C(G)$ be the poset of cyclic subgroups of a finite group $G$ and let $\mathcal{P}$ be the class of $p$-groups of order $p^n$ ($n\ge 3$). Consider the function $α:\mathcal{P}\…