Geodesic
Quasirecognizability by the Set of Element Orders for Groups $^3D_4(q)$ and $F_4(q)$, for $q$ Odd
Algebra i logika, Tome 44 (2005) no. 5, pp. 517-539

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It is proved that if $L$ is one of the simple groups $^3D_4(q)$ or $F_4(q)$, where $q$ is odd, and $G$ is a finite group with the set of element orders as in $L$, then the derived subgroup of $G/F(G)$ is isomorphic to $L$ and the factor group $G/G'$ is a cyclic $\{2,3\}$-group.
Keywords: finite group, set of element orders, quasirecognizability, prime graph.
Mots-clés : simple group 
@article{AL_2005_44_5_a0,
     author = {O. A. Alekseeva and A. S. Kondrat'ev},
     title = {Quasirecognizability by the {Set} of {Element} {Orders} for {Groups~}$^3D_4(q)$ and~$F_4(q)$, for $q${~Odd}},
     journal = {Algebra i logika},
     pages = {517--539},
     publisher = {mathdoc},
     volume = {44},
     number = {5},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2005_44_5_a0/}
}
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O. A. Alekseeva; A. S. Kondrat'ev. Quasirecognizability by the Set of Element Orders for Groups $^3D_4(q)$ and $F_4(q)$, for $q$ Odd. Algebra i logika, Tome 44 (2005) no. 5, pp. 517-539. http://geodesic.mathdoc.fr/item/AL_2005_44_5_a0/