Zeros of $S$-characters
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917497403342848 |
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| author | Breuer, Thomas Joswig, Michael Malle, Gunter |
| author_facet | Breuer, Thomas Joswig, Michael Malle, Gunter |
| contents | The concept of $S$-characters of finite groups was introduced by Zhmud' as a generalisation of transitive permutation characters. Any non-trivial $S$-character takes a zero value on some group element. By a deep result depending on the classification of finite simple groups a non-trivial transitive permutation character even vanishes on some element of prime power order. We present examples that this does not generalise to $S$-characters, thereby answering a question posed by J-P. Serre. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zeros of $S$-characters Breuer, Thomas Joswig, Michael Malle, Gunter Group Theory Representation Theory 20C15, 20D08, 20B05, 11P21, 52B20 The concept of $S$-characters of finite groups was introduced by Zhmud' as a generalisation of transitive permutation characters. Any non-trivial $S$-character takes a zero value on some group element. By a deep result depending on the classification of finite simple groups a non-trivial transitive permutation character even vanishes on some element of prime power order. We present examples that this does not generalise to $S$-characters, thereby answering a question posed by J-P. Serre. |
| title | Zeros of $S$-characters |
| topic | Group Theory Representation Theory 20C15, 20D08, 20B05, 11P21, 52B20 |
| url | https://arxiv.org/abs/2408.16785 |