On the number of non-cyclic subgroups of finite p-groups

Jia Liu, Li Ma, Wei Meng

Let $G$ be a finite $p$-group and $\hat{I}´(G)$ denote the number of all non-cyclic subgroups of $G$. In this paper, an upper bound for $\hat{I}´(G)$ is obtained. Furthermore, we prove that $Î…