Geodesic
Insolubility of finite groups which are isospectral to the alternating group of degree~$10$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 20-24

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Let $G$ be a finite group and $\omega(G)$ the set of all element orders of $G$. We prove that if $\omega(G)=\omega(A_{10})$ where $G$ is a finite group, then $G$ is not-soluble. 
@article{SEMR_2008_5_a3,
     author = {A. M. Staroletov},
     title = {Insolubility of finite groups which are isospectral to the alternating group of degree~$10$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {20--24},
     publisher = {mathdoc},
     volume = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a3/}
}
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A. M. Staroletov. Insolubility of finite groups which are isospectral to the alternating group of degree~$10$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 20-24. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a3/