The exact number of r-regular elements in finite exceptional groups

Abstract

We calculate the precise number of r-regular elements in the finite exceptional groups. As a corollary we find that the proportion of r-regular elements is at least 3577/18432 and for all ε>0, there are infinitely finite simple exceptional groups such that the proportion of r-regular elements is less than $3577/18432+\epsilon$ for some prime r.

10 pages