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.