Examples of Sum of Element Orders of Finite Groups

Abstract

The area of a finite group $G$ is defined as the sum of its element orders and the prime area of $G$ is the sum of its prime element orders. In this paper, we investigate the area and prime area of all finite abelian groups and of some non-abelian groups such as Hamiltonian groups, Hamiltonian perfect order subset groups, Symmetric groups, Alternating groups and Dihedral groups.

Keywords: sum of element orders, perfect order subset groups, Hamiltonian groups, symmetric groups.