Fixers and stabilizers for Ree groups

Abstract

Let $G$ be a finite permutation group on $\Omega ,$ a subgroup $K⩽G$ is called a fixer if each element in $K$ fixes some element in $\Omega .$ In this paper, we characterize fixers $K$ with $|K|⩾|G_{\omega }|$ for each primitive action of almost simple group $G$ with socle ${}^2{G}_2(q).$