Seminars & Colloquia Calendar
Fixed point ratios for primitive groups and applications
Tim Burness, University of Bristol
Location: Hill Center 425
Date & time: Wednesday, 30 March 2022 at 2:00PM - 3:00PM
Abstract: Let G be a finite permutation group and recall that the fixed point ratio of an element x, denoted fpr(x), is the proportion of points fixed by x. Fixed point ratios for finite primitive groups have been studied for many decades, finding a wide range of applications. In this talk, I will present some of the main results and applications, focussing on recent joint work with Bob Guralnick where we determine the triples (G,x,r) such that G is primitive, x has prime order r and fpr(x) > 1/(r+1). The latter result allows us to prove new results on the minimal degree and minimal index of primitive groups, and we have used it in joint work with Moreto and Navarro to study the commuting probability of p-elements in finite groups.