Work

Conjugacy classes of derangements in finite groups of Lie type

Year: 2025

Type: article

Abstract: Let G G be a finite almost simple group of Lie type acting faithfully and primitively on a set Ω \Omega . We prove an analogue of the Boston–Shalev conjecture for conjugacy classes: the proportion of conjugacy classes of G 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).

Source: Transactions of the American Mathematical Society Series B

DOI: 10.1090/btran/193

Authors: Sean Eberhard, Daniele Garzoni

Institutions: Queen's University Belfast, University of Warwick, University of Southern California

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,750

Funders: Royal Society, European Commission, Israel Science Foundation, European Research Council