Title: On the resolvent degree of PSU(3,q) Show Chinese title

Title: 关于PSU(3,q)的预解式次数

Abstract: 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 G\'{o}mez-Gonz\'{a}les-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 $q$. Show Chinese abstract

Abstract: 预解次数（$\operatorname{RD}$）是有限群的一个不变量，反映了其代数作用的复杂性。 我们利用Gómez-Gonzáles-Sutherland-Wolfson建立的方法，针对所有有限单群，研究了$\operatorname{RD}(G)$的界限问题，这些方法涉及$\operatorname{RD}^{\leq d}_{\mathbb{C}}$-普遍性和特殊点。 我们给出了$\operatorname{RD}(\operatorname{PSU}(3,q))$和$\operatorname{RD}(\operatorname{PSU}(2, q))$的上界，这些上界基于经典不变量理论。 在$\operatorname{PSU}(3,q)$的情况下，低次数不变量的稳定性允许$\operatorname{RD}$在$q$中增长的渐近界。