Tărnăuceanu Marius

A density result on the sum of element orders of a finite group

Let $\mathcal{G}$ be the class of all finite groups and consider the function $ψ'':\mathcal{G}\longrightarrow(0,1]$, given by $ψ''(G)=\frac{ψ(G)}{|G|^2}$, where $ψ(G)$ is the sum of element orders of a finite group $G$. In this paper, we show that the image of $ψ''$ is a dense set in $[0, 1]$. Also, we study the injectivity and the surjectivity of $ψ''$.