CHARACTERIZATION OF A5 AND PSL(2; 7) BY SUM OF ELEMENT ORDERS

Abstract. let g be a finite group. we denote by (g) the integer pg2g o(g), where o(g) denotesthe order of g 2 g. here we show that (a5) < (g) for every non-simple group g of order 60, wherea5 is the alternating group of degree 5. also we prove that (psl(2; 7)) < (g) for all non-simplegroups g of order 168. these two results confirm the conjecture posed in [j. algebra appl., 10 no. 2(2011) 187-190] for simple groups a5 and psl(2; 7).