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arXiv · 2603.16498

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

Jia Liu·Li Ma·Wei Meng
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Abstract

Let $G$ be a finite $p$-group and $δ(G)$ denote the number of all non-cyclic subgroups of $G$. In this paper, an upper bound for $δ(G)$ is obtained. Furthermore, we prove that $δ(G)\leq δ(M_p(1, 1, 1) \times C_{p}^{n-3})$ (if $p=2$, then $δ(G)\leq δ(D_8\times C_{2}^{n-3})$), for any non-elementary abelian $p$-group $G$ of order $p^n$.

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Jia Liu, Li Ma, Wei Meng. 2026-03-17. On the number of non-cyclic subgroups of finite p-groups. https://arxiv.org/abs/2603.16498

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