Geodesic
Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum
Algebra i logika, Tome 47 (2008) no. 1, pp. 83-93

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It is proved that finite simple groups $L_4(2^m)$, $m\ge2$, and $U_4(2^m)$, $m\ge2$, are, up to isomorphism, recognized by spectra, i.e., sets of their element orders, in the class of finite groups. As a consequence the question on recognizability by spectrum is settled for all finite simple groups without elements of order 8.
Keywords: finite simple group, spectrum of group. 
@article{AL_2008_47_1_a4,
     author = {V. D. Mazurov and G. Y. Chen},
     title = {Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum},
     journal = {Algebra i logika},
     pages = {83--93},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2008_47_1_a4/}
}
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V. D. Mazurov; G. Y. Chen. Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum. Algebra i logika, Tome 47 (2008) no. 1, pp. 83-93. http://geodesic.mathdoc.fr/item/AL_2008_47_1_a4/