# Derangements in permutation groups

Seminar

Speaker

Daniele Garzoni (Tel Aviv University)

Date

22/03/2023 - 11:30 - 10:30Add to Calendar

`2023-03-22 10:30:00``2023-03-22 11:30:00``Derangements in permutation groups``Given a group G acting on a set X, an element g of G is called a derangement if it acts without fixed points on X. The Boston--Shalev conjecture, proved by Fulman and Guralnick, asserts that in a finite simple group G acting transitively on X, the proportion of derangements is at least some absolute constant c > 0. We will first give an introduction to the subject, highlighting some connections with number theory. Then, we will see a version of this conjecture for the proportion of *conjugacy classes* containing derangements in finite groups of Lie type. Joint work with Sean Eberhard. ================================================ https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062``Third floor seminar room, Mathematics building, and on Zoom. See link below.``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room, Mathematics building, and on Zoom. See link below.

Abstract

Given a group G acting on a set X, an element g of G is called a derangement if it acts without fixed points on X. The Boston--Shalev conjecture, proved by Fulman and Guralnick, asserts that in a finite simple group G acting transitively on X, the proportion of derangements is at least some absolute constant c > 0. We will first give an introduction to the subject, highlighting some connections with number theory. Then, we will see a version of this conjecture for the proportion of *conjugacy classes* containing derangements in finite groups of Lie type. Joint work with Sean Eberhard.

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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 22/03/2023