Geodesic
On the definability of the group $L_2(7)$ by its spectrum
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 250-252

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For a group $G$, denote by $\omega(G)$ the spectrum of $G$, i.e., the set of its element orders. We prove that every group $G$ with $\omega(G)\subseteq\omega(L_2(7))=\{1,2,3,4,7\}$ in which the product of every two involutions is a $2$-element contains a normal $2$-subgroup with primary quotient. We also reduce the investigation of groups $G$ with $\omega(G)=\omega(L_2(7))$ to that of groups generated by involutions. 
@article{SEMR_2005_2_a31,
     author = {A. A. Kuznetsov},
     title = {On the definability of the group $L_2(7)$ by its spectrum},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {250--252},
     publisher = {mathdoc},
     volume = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a31/}
}
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A. A. Kuznetsov. On the definability of the group $L_2(7)$ by its spectrum. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 250-252. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a31/