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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19237 |
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| _version_ | 1866912750610939904 |
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| author | Christofferson, Pablo Nicolas Ganguly, Akash Gomez-Gonzales, Claudio Kuriyama, Ella Li, Yihan Carmen Baydoun, Nawal |
| author_facet | Christofferson, Pablo Nicolas Ganguly, Akash Gomez-Gonzales, Claudio Kuriyama, Ella Li, Yihan Carmen Baydoun, Nawal |
| contents | Resolvent degree ($\operatorname{RD}$) is an invariant of finite groups in terms of the complexity of their algebraic actions. We address the problem of bounding $\operatorname{RD}(G)$ for all finite simple groups using the methods established by Gómez-Gonzáles-Sutherland-Wolfson in terms of $\operatorname{RD}^{\leq d}_{\mathbb{C}}$-versality and special points. We give upper bounds on $\operatorname{RD}(\operatorname{PSU}(3,q))$ and $\operatorname{RD}(\operatorname{PSU}(2, q))$ in terms of classical invariant theory. In the $\operatorname{PSU}(3,q)$ case, stability of low-degree invariants permit an asymptotic bound on $\operatorname{RD}$ growing in $q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the resolvent degree of PSU(3,q) Christofferson, Pablo Nicolas Ganguly, Akash Gomez-Gonzales, Claudio Kuriyama, Ella Li, Yihan Carmen Baydoun, Nawal Group Theory Algebraic Geometry 14L30 (Primary), 13A50, 20C25, 20C33 (Secondary) Resolvent degree ($\operatorname{RD}$) is an invariant of finite groups in terms of the complexity of their algebraic actions. We address the problem of bounding $\operatorname{RD}(G)$ for all finite simple groups using the methods established by Gómez-Gonzáles-Sutherland-Wolfson in terms of $\operatorname{RD}^{\leq d}_{\mathbb{C}}$-versality and special points. We give upper bounds on $\operatorname{RD}(\operatorname{PSU}(3,q))$ and $\operatorname{RD}(\operatorname{PSU}(2, q))$ in terms of classical invariant theory. In the $\operatorname{PSU}(3,q)$ case, stability of low-degree invariants permit an asymptotic bound on $\operatorname{RD}$ growing in $q$. |
| title | On the resolvent degree of PSU(3,q) |
| topic | Group Theory Algebraic Geometry 14L30 (Primary), 13A50, 20C25, 20C33 (Secondary) |
| url | https://arxiv.org/abs/2509.19237 |