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

	Characterization of A₅ and PSL(2, 7) by sum of element orders
International Journal of Group Theory
مقاله 5، دوره 2، شماره 2، شهریور 2013، صفحه 35-39 اصل مقاله (381.87 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.1918
نویسنده
Seyyed Majid Jafarian Amiri^*
Department of Mathematics, Faculty of Sciences, University of Zanjan
چکیده
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 $PSL(2,7)$‎.
کلیدواژه‌ها
Finite groups؛ simple group؛ element orders

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