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) denotes the order of g 2 G. Here we show that (A5) < (G) for every non-simple group G of order 60, where A5 is the alternating group of degree 5. Also we prove that (PSL(2; 7)) < (G) for all non-simple groups 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).