An exact upper bound for sums of element orders in non-cyclic finite groups

Marcel Herzog, Patrizia Longobardi, Mercede Maj

Denote the sum of element orders in a finite group $G$ by $\psi (G)$ and let $C_n$ denote the cyclic group of order $n$. Suppose that $G$ is a non-cyclic finite group of order $n$ and…