Geodesic
Recognition by spectrum for finite simple groups with orders having prime divisors at most 17
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 14-20

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The spectrum $\omega(G)$ of a group $G$ is the set of its element orders. We write $h(G)$ to denote the number of pairwise non-isomorphic finite groups $H$ with $\omega(H)=\omega(G)$. We say that $G$ is recognizable by spectrum if $h(G)=1$ and that $G$ is a group with solved recognition-by-spectrum problem if $h(G)$ is known. In the paper we prove that the groups $C_3(4)$ and $D_4(4)$ are recognizable by spectrum. It follows from this result that the recognition-by-spectrum problem is solved for all finite simple groups with orders having prime divisors at most $17$.
Keywords: finite group, spectrum of a group, recognition by spectrum.
Mots-clés : simple group 
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     author = {I. B. Gorshkov},
     title = {Recognition by spectrum for finite simple groups with orders having prime divisors at most 17},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {14--20},
     publisher = {mathdoc},
     volume = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a1/}
}
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I. B. Gorshkov. Recognition by spectrum for finite simple groups with orders having prime divisors at most 17. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 14-20. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a1/