Some Remarks on Super $M_{p}$-groups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917254980960256 |
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| author | Chen, Xiaoyou Moghaddamfar, A. R. |
| author_facet | Chen, Xiaoyou Moghaddamfar, A. R. |
| contents | Let $G$ be a finite group and $p$ be a prime divisor of $|G|$. An irreducible $p$-Brauer character $φ$ of $G$ is called super-monomial if every primitive $p$-Brauer character inducing $φ$ is linear. The group $G$ is said to be a super $M_{p}$-group if every irreducible $p$-Brauer character of $G$ is super-monomial. In this note, we investigate the conditions under which a finite group $G$ qualifies as a super $M_{p}$-group. We demonstrate that every normal subgroup of a super $M_{p}$-group of odd order is an $M_{p}$-group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_07172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some Remarks on Super $M_{p}$-groups Chen, Xiaoyou Moghaddamfar, A. R. Group Theory 20C20, 20C15 Let $G$ be a finite group and $p$ be a prime divisor of $|G|$. An irreducible $p$-Brauer character $φ$ of $G$ is called super-monomial if every primitive $p$-Brauer character inducing $φ$ is linear. The group $G$ is said to be a super $M_{p}$-group if every irreducible $p$-Brauer character of $G$ is super-monomial. In this note, we investigate the conditions under which a finite group $G$ qualifies as a super $M_{p}$-group. We demonstrate that every normal subgroup of a super $M_{p}$-group of odd order is an $M_{p}$-group. |
| title | Some Remarks on Super $M_{p}$-groups |
| topic | Group Theory 20C20, 20C15 |
| url | https://arxiv.org/abs/2602.07172 |