Geodesic
Recognizability of alternating groups by spectrum
Algebra i logika, Tome 52 (2013) no. 1, pp. 57-63

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The spectrum of a group is the set of its element orders. A finite group $G$ is said to be recognizable by spectrum if every finite group that has the same spectrum as $G$ is isomorphic to $G$. It is proved that simple alternating groups An are recognizable by spectrum, for $n\ne6,10$. This implies that every finite group whose spectrum coincides with that of a finite non-Abelian simple group has at most one non-Abelian composition factor.
Keywords: finite group, alternating group, spectrum of group, recognizability by spectrum.
Mots-clés : simple group 
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     author = {I. B. Gorshkov},
     title = {Recognizability of alternating groups by spectrum},
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     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_1_a3/}
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I. B. Gorshkov. Recognizability of alternating groups by spectrum. Algebra i logika, Tome 52 (2013) no. 1, pp. 57-63. http://geodesic.mathdoc.fr/item/AL_2013_52_1_a3/