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 $PSL(2,7)$.
H. Amiri, S. M. Jafarian Amiri and I. M. Isaacs (2009). Sums of element orders in finite groups. Comm. Algebra. 37 (9), 2978-2980 H. Amiri and S. M. Jafarian Amiri (2011). Sum of element orers on finite groups of the same order. J. Algebra Appl.. 10 (2), 187-190
Jafarian Amiri, S. M. (2013). Characterization of A5 and PSL(2, 7) by sum of element orders. International Journal of Group Theory, 2(2), 35-39. doi: 10.22108/ijgt.2013.1918
MLA
Seyyed Majid Jafarian Amiri. "Characterization of A5 and PSL(2, 7) by sum of element orders". International Journal of Group Theory, 2, 2, 2013, 35-39. doi: 10.22108/ijgt.2013.1918
HARVARD
Jafarian Amiri, S. M. (2013). 'Characterization of A5 and PSL(2, 7) by sum of element orders', International Journal of Group Theory, 2(2), pp. 35-39. doi: 10.22108/ijgt.2013.1918
VANCOUVER
Jafarian Amiri, S. M. Characterization of A5 and PSL(2, 7) by sum of element orders. International Journal of Group Theory, 2013; 2(2): 35-39. doi: 10.22108/ijgt.2013.1918
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