Geodesic
Characterization of $L_3(2^n)$ by Sylow 2-subgroups
Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 519-524.

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The following theorem is proved: If the Sylow 2-subgroups of a finite simple group $G$ are isomorphic to the Sylow 2-subgroups of $L_3(2^n)$, $n\geqslant2$, then $G$ is isomorphic with $L_3(2^n)$. 
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V. D. Mazurov; S. A. Syskin. Characterization of $L_3(2^n)$ by Sylow 2-subgroups. Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 519-524. http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a5/

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