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Article

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. (English). Archivum Mathematicum, vol. 43 (2007), issue 1, pp. 31-37
MSC: 20D06, 20D60 | MR 2310122 | Zbl 1156.20013
Keywords:
projective special linear group; element order
Summary:
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.
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