On the number of non-cyclic subgroups of finite p-groups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915869883367424 |
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| author | Liu, Jia Ma, Li Meng, Wei |
| author_facet | Liu, Jia Ma, Li Meng, Wei |
| contents | 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 $p^n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_16498 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the number of non-cyclic subgroups of finite p-groups Liu, Jia Ma, Li Meng, Wei Group Theory 20D15, 20D30 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 $p^n$. |
| title | On the number of non-cyclic subgroups of finite p-groups |
| topic | Group Theory 20D15, 20D30 |
| url | https://arxiv.org/abs/2603.16498 |