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.

Key Words:

• Element orders
• Finite group

2010 Mathematics Subject Classification:

• 20D60

ACKNOWLEDGMENT

The authors is indebted to the referee for his/her careful reading and valuable comments. This research was in part supported by a grant from university of Zanjan.

Notes

Communicated by A. Turull.