Geodesic
Recognizability of symmetric groups by spectrum
Algebra i logika, Tome 53 (2014) no. 6, pp. 693-703

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The spectrum of a finite group is the set of its element orders. A finite group $G$ is said to be recognizable by spectrum if every finite group whose spectrum coincides with the spectrum of $G$ is isomorphic to $G$. It is proved the symmetric group $S_n$ is recognizable by spectrum for $n\not\in\{2,3,4,5,6,8,10,15,16,18,21,27,33,35,39,45\}$.
Keywords: finite group, symmetric group, spectrum of group, recognition by spectrum.
Mots-clés : simple group 
@article{AL_2014_53_6_a1,
     author = {I. B. Gorshkov},
     title = {Recognizability of symmetric groups by spectrum},
     journal = {Algebra i logika},
     pages = {693--703},
     publisher = {mathdoc},
     volume = {53},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2014_53_6_a1/}
}
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I. B. Gorshkov. Recognizability of symmetric groups by spectrum. Algebra i logika, Tome 53 (2014) no. 6, pp. 693-703. http://geodesic.mathdoc.fr/item/AL_2014_53_6_a1/