Zeros of characters and orders of elements in finite groups
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arXiv
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| Format: | Preprint |
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2026
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| author | Malle, Gunter Navarro, Gabriel Tiep, Pham Huu |
| author_facet | Malle, Gunter Navarro, Gabriel Tiep, Pham Huu |
| contents | We investigate a beautiful conjecture of T. Wilde on character values and element orders of finite groups. We reduce it to a statement on nearly simple groups that can be checked ``prime by prime". For these groups, we show that a strong form of Wilde's conjecture holds in many important cases, and for primes $p>5$ we are able to show the required statement for most classes of nearly simple groups. The few remaining cases, however, seem to require information on extensions of irreducible characters that are not available at the present time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04513 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zeros of characters and orders of elements in finite groups Malle, Gunter Navarro, Gabriel Tiep, Pham Huu Representation Theory Group Theory Primary 20C15, 20C33, Secondary 20C20, 20D06 We investigate a beautiful conjecture of T. Wilde on character values and element orders of finite groups. We reduce it to a statement on nearly simple groups that can be checked ``prime by prime". For these groups, we show that a strong form of Wilde's conjecture holds in many important cases, and for primes $p>5$ we are able to show the required statement for most classes of nearly simple groups. The few remaining cases, however, seem to require information on extensions of irreducible characters that are not available at the present time. |
| title | Zeros of characters and orders of elements in finite groups |
| topic | Representation Theory Group Theory Primary 20C15, 20C33, Secondary 20C20, 20D06 |
| url | https://arxiv.org/abs/2605.04513 |