Character estimates for finite classical groups and the asymptotic Thompson Conjecture
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916846807023616 |
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| author | Larsen, Michael Tiep, Pham Huu |
| author_facet | Larsen, Michael Tiep, Pham Huu |
| contents | If $G$ is a finite classical group, linear or unitary in any characteristic, and orthogonal in odd characteristic, we give an approximate formula for $χ(g)$ in which the error term is much smaller than the estimate, when $g\in G$ is an element with large centralizer and $χ\in \mathrm{Irr}(G)$ is an irreducible character of low degree. As an application, we prove Thompson's conjecture for all sufficiently large finite simple groups: each such group contains a conjugacy class whose square is the whole group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09047 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Character estimates for finite classical groups and the asymptotic Thompson Conjecture Larsen, Michael Tiep, Pham Huu Group Theory 20C33 (Primary) 20C15, 20C30, 20P05 (Secondary) If $G$ is a finite classical group, linear or unitary in any characteristic, and orthogonal in odd characteristic, we give an approximate formula for $χ(g)$ in which the error term is much smaller than the estimate, when $g\in G$ is an element with large centralizer and $χ\in \mathrm{Irr}(G)$ is an irreducible character of low degree. As an application, we prove Thompson's conjecture for all sufficiently large finite simple groups: each such group contains a conjugacy class whose square is the whole group. |
| title | Character estimates for finite classical groups and the asymptotic Thompson Conjecture |
| topic | Group Theory 20C33 (Primary) 20C15, 20C30, 20P05 (Secondary) |
| url | https://arxiv.org/abs/2403.09047 |