The average element order and the number of conjugacy classes of finite groups

E. I. Khukhro, A. Moretó, M. Zarrin

Let $o(G)$ be the average order of the elements of $G$, where $G$ is a finite group. We show that there is no polynomial lower bound for $o(G)$ in terms of $o(N)$, where $N\triangl…