A characterization of the simple group $PSL_5(5)$ by the set of its element orders

M. R. Darafsheh^a, A. Sadrudini<sup>b

a</sup> School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran
^b Department of Mathematics, Tarbiat Modarres University

Abstract: Let $G$ be a finite group and let $\omega(G)$ denote the set of the element orders of $G$. For the simple group $PSL_5(5)$ we prove that if $G$ is a finite group with $\omega(G)=\omega(PSL_5(5))$, then either $G\cong PSL_5(5)$ or $G\cong PSL_5(5):\langle\theta\rangle$ where $\theta$ is a graph automorphism of $PSL_5(5)$ of order 2.

Keywords: projective special linear group, element order.

UDC: 519.542

Received: 16.08.2006

 English version: Siberian Mathematical Journal, 2008, 49:3, 418–422

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