Fixed point ratios, Sylow numbers and coverings of $p$-elements in finite groups
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909273636732928 |
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| author | Guralnick, Robert M. Maróti, Attila Madrid, Juan Martínez Moretó, Alexander Rizo, Noelia |
| author_facet | Guralnick, Robert M. Maróti, Attila Madrid, Juan Martínez Moretó, Alexander Rizo, Noelia |
| contents | Fixed point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a prime $p$ and a finite group $G$, we use fixed point ratios to study the number of Sylow $p$-subgroups of $G$ and the minimal size of a covering by proper subgroups of the set of $p$-elements of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20355 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fixed point ratios, Sylow numbers and coverings of $p$-elements in finite groups Guralnick, Robert M. Maróti, Attila Madrid, Juan Martínez Moretó, Alexander Rizo, Noelia Group Theory Fixed point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a prime $p$ and a finite group $G$, we use fixed point ratios to study the number of Sylow $p$-subgroups of $G$ and the minimal size of a covering by proper subgroups of the set of $p$-elements of $G$. |
| title | Fixed point ratios, Sylow numbers and coverings of $p$-elements in finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2407.20355 |