##
A characterization property of the simple group $PSL_{4}(5)$ by the set of its element orders

##
*
Mohammad Reza Darafsheh, Yaghoub Farjami, Abdollah Sadrudini
*

** Address.**
Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Tehran

Department of Mathematics, Tarbiat Modarres University, P.O. Box 14115-137, Tehran, Iran

** E-mail:**
darafsheh@ut.ac.ir

**Abstract.**
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.

**AMSclassification. ** Primary 20D06, Secondary 20H30.

**Keywords. ** Projective special linear group, element order.