Conjugacy classes of derangements in finite groups of Lie type

2023/02/03 by Sean Eberhard, Eberhard, Sean, Daniele Garzoni +1 · 1 citation
Chemistry · Mathematics · #Advanced Algebra and Geometry #Crystal structures of chemical compounds #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.01655

openalex publication_date 2023/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite almost simple group of Lie type acting faithfully and primitively on a set Ω. We prove an analogue of the Boston--Shalev conjecture for conjugacy classes: the proportion of conjugacy classes of G consisting of derangements is bounded away from zero. This answers a question of Guralnick and Zalesski. The proof is based on results on the anatomy of palindromic polynomials over finite fields (with either reflective symmetry or conjugate-reflective symmetry).

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• Derangements in finite classical groups and characteristic polynomials of random matrices

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