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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.23637 |
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| _version_ | 1866908290601975808 |
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| author | Herbig, Christopher |
| author_facet | Herbig, Christopher |
| contents | In [3, Theorem 6.7B], the authors use the Main Theorems of Brauer to give a proof of Burnside's Normal $p$-complement Theorem. Unfortunately, the proof contains an error. We take this opportunity to give a proof along similar lines, circumventing the error by means of a well-known result on traces of totally positive cyclotomic integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Block-theoretic Proof of Burnside's Normal $p$-complement Theorem Herbig, Christopher Group Theory 20C15 (Primary) 20C20 In [3, Theorem 6.7B], the authors use the Main Theorems of Brauer to give a proof of Burnside's Normal $p$-complement Theorem. Unfortunately, the proof contains an error. We take this opportunity to give a proof along similar lines, circumventing the error by means of a well-known result on traces of totally positive cyclotomic integers. |
| title | A Block-theoretic Proof of Burnside's Normal $p$-complement Theorem |
| topic | Group Theory 20C15 (Primary) 20C20 |
| url | https://arxiv.org/abs/2503.23637 |