Character formula for conjugacy classes in a coset
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914245874024448 |
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| author | Dokchitser, Tim Dokchitser, Vladimir |
| author_facet | Dokchitser, Tim Dokchitser, Vladimir |
| contents | Let $G$ be a finite group and $N<G$ a normal subgroup with $G/N$ abelian. We show how the conjugacy classes of $G$ in a given coset $qN$ relate to the irreducible characters of $G$ that are not identically $0$ on $qN$. We describe several consequences. In particular, we deduce that when $G/N$ is cyclic generated by $q$, the number of irreducible characters of $N$ that extend to $G$ is the number of conjugacy classes of $G$ in $qN$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_07247 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Character formula for conjugacy classes in a coset Dokchitser, Tim Dokchitser, Vladimir Group Theory 20C15, 20E45 (Primary), 20C25, 20K35 (Secondary) Let $G$ be a finite group and $N<G$ a normal subgroup with $G/N$ abelian. We show how the conjugacy classes of $G$ in a given coset $qN$ relate to the irreducible characters of $G$ that are not identically $0$ on $qN$. We describe several consequences. In particular, we deduce that when $G/N$ is cyclic generated by $q$, the number of irreducible characters of $N$ that extend to $G$ is the number of conjugacy classes of $G$ in $qN$. |
| title | Character formula for conjugacy classes in a coset |
| topic | Group Theory 20C15, 20E45 (Primary), 20C25, 20K35 (Secondary) |
| url | https://arxiv.org/abs/2105.07247 |