Finite groups with few conjugate classes of minimal non-abelian subgroups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912536009375744 |
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| author | Qu, Haipeng Zhang, Junqiang |
| author_facet | Qu, Haipeng Zhang, Junqiang |
| contents | Let $G$ be a finite non-abelian group and $κ_1(G)$ the number of conjugate classes of minimal non-abelian subgroups of $G$. The structure of $G$ with $κ_1(G)=1$ is determined. In the case of $G$ being the $p$-groups, the structure of $G$ with $κ_1(G)\leqslant p$ is also determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite groups with few conjugate classes of minimal non-abelian subgroups Qu, Haipeng Zhang, Junqiang Group Theory 20D15, 20D20 Let $G$ be a finite non-abelian group and $κ_1(G)$ the number of conjugate classes of minimal non-abelian subgroups of $G$. The structure of $G$ with $κ_1(G)=1$ is determined. In the case of $G$ being the $p$-groups, the structure of $G$ with $κ_1(G)\leqslant p$ is also determined. |
| title | Finite groups with few conjugate classes of minimal non-abelian subgroups |
| topic | Group Theory 20D15, 20D20 |
| url | https://arxiv.org/abs/2508.09706 |