Fixers and stabilizers for Ree groups

Abstract

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