Characters, Hall subgroups, and Normal Complements
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909273453232128 |
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| author | Guralnick, Robert Navarro, Gabriel |
| author_facet | Guralnick, Robert Navarro, Gabriel |
| contents | If $H$ is a Hall subgroup of a finite group $G$, it was proven in 1989 using the classification of finite simple groups that all the irreducible complex characters of $H$ extend to $G$ if and only if there is $N\trianglelefteq G$ such that $HN=G$ and $H\cap N=1$. In this note we offer a modular version of this result under more general hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characters, Hall subgroups, and Normal Complements Guralnick, Robert Navarro, Gabriel Group Theory Representation Theory 20C15 If $H$ is a Hall subgroup of a finite group $G$, it was proven in 1989 using the classification of finite simple groups that all the irreducible complex characters of $H$ extend to $G$ if and only if there is $N\trianglelefteq G$ such that $HN=G$ and $H\cap N=1$. In this note we offer a modular version of this result under more general hypothesis. |
| title | Characters, Hall subgroups, and Normal Complements |
| topic | Group Theory Representation Theory 20C15 |
| url | https://arxiv.org/abs/2406.16184 |