Finite groups with many normalizers
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909557474721792 |
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| author | Tărnăuceanu, Marius |
| author_facet | Tărnăuceanu, Marius |
| contents | A group $G$ is said to have dense normalizers if each non-empty open interval in its subgroup lattice $L(G)$ contains the normalizer of a certain subgroup of $G$. In this note, we find all finite groups satisfying this property. We also classify the finite groups in which $k$ subgroups are not normalizers, for $k=1,2,3,4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite groups with many normalizers Tărnăuceanu, Marius Group Theory A group $G$ is said to have dense normalizers if each non-empty open interval in its subgroup lattice $L(G)$ contains the normalizer of a certain subgroup of $G$. In this note, we find all finite groups satisfying this property. We also classify the finite groups in which $k$ subgroups are not normalizers, for $k=1,2,3,4$. |
| title | Finite groups with many normalizers |
| topic | Group Theory |
| url | https://arxiv.org/abs/2503.22966 |