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arXiv · 2302.01655

Conjugacy classes of derangements in finite groups of Lie type

Sean Eberhard·Daniele Garzoni
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Abstract

Let $G$ be a finite almost simple group of Lie type acting faithfully and primitively on a set $\Omega$. 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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Sean Eberhard, Daniele Garzoni. 2023-02-03. Conjugacy classes of derangements in finite groups of Lie type. https://doi.org/10.1090/btran%2F193

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