On $G$-character tables for normal subgroups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916399213969408 |
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| author | Felipe, María José Pérez-Ramos, María Dolores Sotomayor, Víctor |
| author_facet | Felipe, María José Pérez-Ramos, María Dolores Sotomayor, Víctor |
| contents | Let $N$ be a normal subgroup of a finite group $G$. From a result due to Brauer, it can be derived that the character table of $G$ contains square submatrices which are induced by the $G$-conjugacy classes of elements in $N$ and the $G$-orbits of irreducible characters of $N$. In the present paper, we provide an alternative approach to this fact through the structure of the group algebra. We also show that such matrices are non-singular and become a useful tool to obtain information of $N$ from the character table of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11591 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $G$-character tables for normal subgroups Felipe, María José Pérez-Ramos, María Dolores Sotomayor, Víctor Group Theory 20C15, 20E45, 20C05 Let $N$ be a normal subgroup of a finite group $G$. From a result due to Brauer, it can be derived that the character table of $G$ contains square submatrices which are induced by the $G$-conjugacy classes of elements in $N$ and the $G$-orbits of irreducible characters of $N$. In the present paper, we provide an alternative approach to this fact through the structure of the group algebra. We also show that such matrices are non-singular and become a useful tool to obtain information of $N$ from the character table of $G$. |
| title | On $G$-character tables for normal subgroups |
| topic | Group Theory 20C15, 20E45, 20C05 |
| url | https://arxiv.org/abs/2409.11591 |