Second Maximum Sum of Element Orders of Finite Nilpotent Groups

Abstract

In [1], the authors proved that the maximum sum of element orders on finite groups of the same order occurs in cyclic group. In this paper we obtain the structure of groups having maximum sum of element orders on noncyclic nilpotent group of the same order.

Key Words:

• Element orders
• Finite groups
• Nilpotent groups

2000 Mathematics Subject Classification:

• Primary 20DXX
• Secondary 20D15

ACKNOWLEDGMENT

The author is indebted to the referee for his/her careful reading and valuable comments.

Notes

Communicated by A. Turull.