Some Properties on Sums of Element Orders in Finite p-groups

Abstract

In literature, there are many papers on the sum of element orders of a finite group. In this study,in particular, we deal with the cases in finite p-groups. Our main aim is to investigate the sums ofelement orders in finite p-groups and to give some properties of such sums. Let ψ(G) denote the sum ofelement orders of a finite group G. As an immediate consequence, we proved that ψ(G)