Geodesic
Recognizing Groups $G_2(3^n)$ by Their Element Orders
Algebra i logika, Tome 41 (2002) no. 2, pp. 130-142

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It is proved that a finite group that is isomorphic to a simple non-Abelian group $G=G_2(3^n)$ is, up to isomorphism, recognized by a set $\omega(G)$ of its element orders, that is, $H \simeq G$ if $\omega(H)=\omega(G)$ for some finite group $H$.
Keywords: finite group, recognizability of groups by their element orders.
Mots-clés : simple non-Abelian group 
@article{AL_2002_41_2_a1,
     author = {A. V. Vasil'ev},
     title = {Recognizing {Groups} $G_2(3^n)$ by {Their} {Element} {Orders}},
     journal = {Algebra i logika},
     pages = {130--142},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_2_a1/}
}
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A. V. Vasil'ev. Recognizing Groups $G_2(3^n)$ by Their Element Orders. Algebra i logika, Tome 41 (2002) no. 2, pp. 130-142. http://geodesic.mathdoc.fr/item/AL_2002_41_2_a1/