University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 Characterization of A5 and PSL(2, 7) by sum of element orders 35 39 1918 10.22108/ijgt.2013.1918 EN Seyyed Majid Jafarian Amiri Department of Mathematics, Faculty of Sciences, University of Zanjan Journal Article 2012 05 13 Let $G$ be a finite group‎. ‎We denote by $\psi(G)$ the integer $\sum_{g\in G}o(g)$‎, ‎where $o(g)$ denotes the order of $g \in G$‎. ‎Here we show that‎ ‎$\psi(A_5)< \psi(G)$ for every non-simple group $G$ of order $60$‎, ‎where $A_5$ is the alternating group of degree $5$‎. ‎Also we prove that $\psi(PSL(2,7))<\psi(G)$ for all non-simple‎ ‎groups $G$ of order $168$‎. ‎These two results confirm the conjecture‎ ‎posed in [J‎. ‎Algebra Appl.‎, ‎{\bf 10} No‎. ‎2 (2011) 187-190] for simple groups $A_5$ and $PSL(2,7)$‎. https://ijgt.ui.ac.ir/article_1918_b2e767f38421bf016428f8625e625431.pdf