Geodesic
On recognition by spectrum of symmetric groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 111-121

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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 with the same spectrum is isomorphic to $G$. We prove that if $n\in\{15,16,18,21,27\}$ then symmetric groups $Sym_n$ are recognizable by spectrum.
Keywords: finite group, symmetric group, spectrum of a group, recognizability by spectrum.
Mots-clés : simple group 
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     author = {I. B. Gorshkov and A. N. Grishkov},
     title = {On recognition by spectrum of symmetric groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {111--121},
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     volume = {13},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a2/}
}
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I. B. Gorshkov; A. N. Grishkov. On recognition by spectrum of symmetric groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 111-121. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a2/