Bulletin of the
Korean Mathematical Society BKMS

For a finite group $G$, let $\psi(G)$ denote the sum of element orders of $G$. If $\psi^{\prime\prime}(G)=\dfrac{\psi(G)}{|G|^2} $, we show here that the image of $\psi^{\prime\prime}$ on the class of all Dihedral groups whose order is twice a composite number greater than 4 is dense in $[0,\frac{1}{4}]$. We also derive some properties of $\psi^{\prime\prime}$ on the class of all Dihedral groups whose order is twice a prime number.

Keywords: sum of element orders, Dihedral groups

MSC numbers: 20D30, 20E34, 40A05, 03E20