Characterization of A5 and PSL(2,7) by sum of elements orders

Abstract

Let $G$ be a finite group. We denote $psi(G)=sum_{gin G}o(g)$ where $o(g)$ denotes the order of $g in G$. Here we show that $psi(A_5)< psi(G)$ for every nonsimple group $G$ of order 60. Also we prove that $psi(PSL(2,7))groups $G$ of order 168. These two results confirm the conjecture posed in [2] for simple groups $A_5$ and $PSL(2,7)$.

Keywords

• finite groups
• simple group
• element orders