Finite groups whose subgroup graph contains a vertex of large degree
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912218632683520 |
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| author | Tărnăuceanu, Marius |
| author_facet | Tărnăuceanu, Marius |
| contents | T.C. Burness and S.D. Scott \cite{3} classified finite groups $G$ such that the number of prime order subgroups of $G$ is greater than $|G|/2-1$. In this note, we study finite groups $G$ whose subgroup graph contains a vertex of degree greater than $|G|/2-1$. The classification given for finite solvable groups extends the work of Burness and Scott. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite groups whose subgroup graph contains a vertex of large degree Tărnăuceanu, Marius Group Theory T.C. Burness and S.D. Scott \cite{3} classified finite groups $G$ such that the number of prime order subgroups of $G$ is greater than $|G|/2-1$. In this note, we study finite groups $G$ whose subgroup graph contains a vertex of degree greater than $|G|/2-1$. The classification given for finite solvable groups extends the work of Burness and Scott. |
| title | Finite groups whose subgroup graph contains a vertex of large degree |
| topic | Group Theory |
| url | https://arxiv.org/abs/2412.18087 |