Lawther, Ross and Liebeck, Martin W. and Seitz, Gary M.
(2002)
*Fixed point ratios in actions of finite exceptional groups of lie type.*
Pacific Journal of Mathematics, 205 (2).
pp. 393-464.
ISSN 0030-8730

## Abstract

Let G be a finite exceptional group of Lie type acting transitively on a set Ø. For x in G, the fixed point ratio of x is the proportion of elements of Ø which are fixed by x. We obtain new bounds for such fixed point ratios. When a point-stabilizer is parabolic we use character theory; and in other cases, we use results on an analogous problem for algebraic groups in Lawther, Liebeck & Seitz, 2002. These give dimension bounds on fixed point spaces of elements of exceptional algebraic groups, which we apply by passing to finite groups via a Frobenius morphism.