Normal subgroups and permutation characters: a correction to a proof of Klingen
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909569731526656 |
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| author | Muller, Peter Spiga, Pablo |
| author_facet | Muller, Peter Spiga, Pablo |
| contents | Let $G$ be a finite group. For subgroups $U$ and $V$ let $1_U^G$ and $1_V^G$ be the permutation characters for the action of $G$ on the right cosets of $U$ and $V$, respectively. Let $N$ be a normal subgroup of $G$. Norbert Klingen, in his book, shows that if $1_U^G=1_V^G$, then $1_{NU}^G=1_{NV}^G$. We give a counterexample to an argument in his proof and we give a new proof of this statement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normal subgroups and permutation characters: a correction to a proof of Klingen Muller, Peter Spiga, Pablo Group Theory Let $G$ be a finite group. For subgroups $U$ and $V$ let $1_U^G$ and $1_V^G$ be the permutation characters for the action of $G$ on the right cosets of $U$ and $V$, respectively. Let $N$ be a normal subgroup of $G$. Norbert Klingen, in his book, shows that if $1_U^G=1_V^G$, then $1_{NU}^G=1_{NV}^G$. We give a counterexample to an argument in his proof and we give a new proof of this statement. |
| title | Normal subgroups and permutation characters: a correction to a proof of Klingen |
| topic | Group Theory |
| url | https://arxiv.org/abs/2504.05362 |