Sylow subgroups and the number of irreducible characters of degrees divisible by a prime $p$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915637943599104 |
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| author | Cossey, James P. Lewis, Mark L. Fry, A. A. Schaeffer Tong-Viet, Hung P. |
| author_facet | Cossey, James P. Lewis, Mark L. Fry, A. A. Schaeffer Tong-Viet, Hung P. |
| contents | Let $G$ be a finite group and $p$ a prime. We establish an upper bound for the derived length of a Sylow $p$-subgroup of $G$ in terms of the number of irreducible characters of $G$ whose degrees are divisible by $p$. We also prove that if $B$ is a $p$-block of a finite $p$-solvable group $G$ with defect group $D$, then the derived length of $D$ is at most one more than the number of ordinary irreducible characters of positive height in $B$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sylow subgroups and the number of irreducible characters of degrees divisible by a prime $p$ Cossey, James P. Lewis, Mark L. Fry, A. A. Schaeffer Tong-Viet, Hung P. Group Theory Primary 20C15, Secondary 20D06, 20D10 Let $G$ be a finite group and $p$ a prime. We establish an upper bound for the derived length of a Sylow $p$-subgroup of $G$ in terms of the number of irreducible characters of $G$ whose degrees are divisible by $p$. We also prove that if $B$ is a $p$-block of a finite $p$-solvable group $G$ with defect group $D$, then the derived length of $D$ is at most one more than the number of ordinary irreducible characters of positive height in $B$. |
| title | Sylow subgroups and the number of irreducible characters of degrees divisible by a prime $p$ |
| topic | Group Theory Primary 20C15, Secondary 20D06, 20D10 |
| url | https://arxiv.org/abs/2511.20861 |