Odd square roots and the sum of element orders on Sn and An

Manoj Kumar Singh

For a finite group $G$ let $\psi (G)$ be the sum of the orders of its elements. The quotient $S_n/A_n$ has order two. Hence $\psi (S_n/A_n)=3$. The quantity to be compared with $\psi (S_n)$ is…