$M$-groups and Codegrees; $M_{p}$-groups and Brauer Character Degrees
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910866824232960 |
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| author | Chen, Xiaoyou Lewis, Mark L. |
| author_facet | Chen, Xiaoyou Lewis, Mark L. |
| contents | Let $G$ be a finite group and $p$ be a prime. We prove that if $G$ has three codegrees, then $G$ is an $M$-group. We prove for some prime $p$ that if every irreducible Brauer character of $G$ is a prime, then for every normal subgroup $N$ of $G$ either $G/N$ or $N$ is an $M_p$-group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $M$-groups and Codegrees; $M_{p}$-groups and Brauer Character Degrees Chen, Xiaoyou Lewis, Mark L. Group Theory Primary 20C15, Secondary 20C20 Let $G$ be a finite group and $p$ be a prime. We prove that if $G$ has three codegrees, then $G$ is an $M$-group. We prove for some prime $p$ that if every irreducible Brauer character of $G$ is a prime, then for every normal subgroup $N$ of $G$ either $G/N$ or $N$ is an $M_p$-group. |
| title | $M$-groups and Codegrees; $M_{p}$-groups and Brauer Character Degrees |
| topic | Group Theory Primary 20C15, Secondary 20C20 |
| url | https://arxiv.org/abs/2503.06878 |