Sum of the Products of the Orders of Two Distinct Elements in Finite Groups

Abstract

Let G be a finite group. Then we denote ψ(G) the sum of element orders in G. In [1] it is proved that if G is a non-cyclic group of order n, then ψ(G) < ψ(C n ), where C n is the cyclic group of order n. Here we generalize and improve this result, and also we give an application of this improvement.