Geodesic
Recognizability of groups $G_2(q)$ by spectrum
Algebra i logika, Tome 52 (2013) no. 1, pp. 3-21

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Two groups are said to be isospectral if they have equal sets of element orders. It is proved that for every finite simple exceptional group $L=G_2(q)$ of Lie type, any finite group $G$ isospectral to $L$ must be isomorphic to $L$.
Keywords: finite simple group, exceptional group of Lie type, element order, spectrum of group, recognition by spectrum. 
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     author = {A. V. Vasil'ev and A. M. Staroletov},
     title = {Recognizability of groups $G_2(q)$ by spectrum},
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A. V. Vasil'ev; A. M. Staroletov. Recognizability of groups $G_2(q)$ by spectrum. Algebra i logika, Tome 52 (2013) no. 1, pp. 3-21. http://geodesic.mathdoc.fr/item/AL_2013_52_1_a0/