Geodesic
Isospectral finite simple groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 111-114

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The spectrum of a finite group is the set of its element orders. Two groups are called isospectral if their spectra coincide. It is known that $PSp_6(2)$ is isospectral to $P\Omega^+_8(2)$ and $\Omega_7(3)$ is isospectral to $P\Omega^+_8(3)$. In the present paper we prove that there are no other pairs of non-isomorphic isospectral finite simple groups. In particular, we prove that there are no three finite simple groups with the same spectrum. 
@article{SEMR_2010_7_a9,
     author = {A. A. Buturlakin},
     title = {Isospectral finite simple groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {111--114},
     publisher = {mathdoc},
     volume = {7},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a9/}
}
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A. A. Buturlakin. Isospectral finite simple groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 111-114. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a9/