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.
@article{108047,
author = {Mohammad Reza Darafsheh and Yaghoub Farjami and Abdollah Sadrudini},
title = {A characterization property of the simple group ${\rm PSL}\sb 4(5)$ by the set of its element orders},
journal = {Archivum Mathematicum},
volume = {043},
year = {2007},
pages = {31-37},
zbl = {1156.20013},
mrnumber = {2310122},
language = {en},
url = {http://dml.mathdoc.fr/item/108047}
}
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 043 (2007) pp. 31-37. http://gdmltest.u-ga.fr/item/108047/
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