Geodesic
On finite groups isospectral to the simple groups~$S_4(q)$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 570-584

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The spectrum of a finite group is the set of its element orders. A finite group $G$ is critical with respect to a subset $\omega$ of the natural numbers if $\omega$ coincides with the spectrum of $G$ and does not coincide with the spectra of proper sections of $G$. We study the structure of groups with spectra equal to the spectra of the simple symplectic groups $PSp(4,q)$, where $q > 3$ and $q \neq 5$. In particular, we describe the structure of the groups critical with respect to the spectra of $PSp(4,q)$.
Keywords: finite group, spectrum, critical group, nonabelian simple group. 
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     author = {Yuri V. Lytkin},
     title = {On finite groups isospectral to the simple groups~$S_4(q)$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {570--584},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a15/}
}
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Yuri V. Lytkin. On finite groups isospectral to the simple groups~$S_4(q)$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 570-584. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a15/