3-characterization of the O'Nan–Sims group

The following theorem is proved.
Theorem. Let $G$ be a finite simple group containing an elementary abelian subgroup $E$ of order $9$ with $C_G(E)=E\times F,$ where $F\simeq L_2 (9)$ and $C_G(e)=C_G(E)$ for all $e\in E^\sharp$. Then $G$ is isomorphic to the O'Nan–Sims simple group.
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