On the resolvent degree of PSU(3,q)

2025/09/23 by Pablo Nicolas Christofferson, Christofferson, Pablo Nicolas, Akash Ganguly +9
Computer Science · Mathematics · #Matrix Theory and Algorithms #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2509.19237

Abstract

Resolvent degree (RD) is an invariant of finite groups in terms of the complexity of their algebraic actions. We address the problem of bounding RD(G) for all finite simple groups using the methods established by Gómez-Gonzáles-Sutherland-Wolfson in terms of RD^{≤ d}_ℂ-versality and special points. We give upper bounds on RD(PSU(3,q)) and RD(PSU(2, q)) in terms of classical invariant theory. In the PSU(3,q) case, stability of low-degree invariants permit an asymptotic bound on RD growing in q.

Citations

• A Summary of Known Bounds on the Essential Dimension and Resolvent Degree of Finite Groups
• Generalized Versality, Special Points, and Resolvent Degree for the Sporadic Groups
• Hilbert's 13th Problem for Algebraic Groups
• Upper Bounds on Resolvent Degree via Sylvester's Obliteration Algorithm
• Upper Bounds on Resolvent Degree and Its Growth Rate
• Tschirnhaus transformations after Hilbert
• Resolvent degree, Hilbert's 13th Problem and geometry
• On the maximum orders of elements of finite almost simple groups and\n primitive permutation groups

Related

• Generalized Versality, Special Points, and Resolvent Degree for the Sporadic Groups
• A Summary of Known Bounds on the Essential Dimension and Resolvent Degree of Finite Groups
• A Paper on Calculating the Height and Relational Complexity of the Primitive Actions of PSL₂ (q) and PGL₂ (q)
• Upper Bounds on Resolvent Degree and Its Growth Rate
• Huppert's analogue conjecture for \PSL(3,q) and \PSU(3,q)