Geodesic
On recognition of the projective special linear groups over binary fields
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 253-263.

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The spectrum $\omega(G)$ of a finite group $G$ is the set of element orders of $G$. Let $L$ be the projective special linear group $L_n(2)$ with $n\ge3$. First, for all $n\ge3$ we establish that every finite group $G$ with $\omega(G)=\omega(L)$ has a unique non-abelian composition factor and this factor is isomorphic to $L$. Second, for some special series of integers $n$ we prove that $L$ is recognizable by spectrum, i. e. every finite group $G$ with $\omega(G)=\omega(L)$ is isomorphic to $L$. 
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M. A. Grechkoseeva; M. S. Lucido; V. D. Mazurov; A. R. Moghaddamfar; A. V. Vasil'ev. On recognition of the projective special linear groups over binary fields. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 253-263. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a18/

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