Geodesic
A characterization property of the simple group ${\rm PSL}\sb 4(5)$ by the set of its element orders
Archivum mathematicum, Tome 43 (2007) no. 1, pp. 31-37.

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Let $\omega (G)$ denote the set of element orders of a finite group $G$. If $H$ is a finite non-abelian simple group and $\omega (H)=\omega (G)$ implies $G$ contains a unique non-abelian composition factor isomorphic to $H$, then $G$ is called quasirecognizable by the set of its element orders. In this paper we will prove that the group $PSL_{4}(5)$ is quasirecognizable.
Classification : 20D06, 20D60
Keywords: projective special linear group; element order 
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     title = {A characterization property of the simple group ${\rm PSL}\sb 4(5)$ by the set of its element orders},
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Darafsheh, Mohammad Reza; Farjami, Yaghoub; Sadrudini, Abdollah. A characterization property of the simple group ${\rm PSL}\sb 4(5)$ by the set of its element orders. Archivum mathematicum, Tome 43 (2007) no. 1, pp. 31-37. http://geodesic.mathdoc.fr/item/ARM_2007__43_1_a2/