Character estimates for finite classical groups and the asymptotic Thompson Conjecture

2024/03/14 by Michael Larsen, Larsen, Michael, Pham Huu Tiep +1 · 2 citations
Mathematics · #20C30 #20C33 (Primary) 20C15 #20P05 (Secondary) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2403.09047

openalex publication_date 2024/03/14 · openalex created_date 2024/03/16 · openalex updated_date 2026/07/28

Abstract

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∈ G is an element with large centralizer and χ∈ 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.

Cited by

• Products of strictly hyperbolic conjugacy classes in symplectic groups
• Orders of commutators and Products of conjugacy classes in finite groups

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• Uniform Character Bounds for Finite Classical Groups
• Characters of p'-degree and Thompson's character degree theorem
• Groups with few p'-character degrees
• Short character values on large conjugacy classes
• Character Levels and Character Bounds. II