Upper bounds for the product of element orders of finite groups

Abstract

Let $G$ be a finite group of order $n$, and denote by $\rho (G)$ the product of element orders of $G$. The aim of this work is to provide some upper bounds for $\rho (G)$ depending only on $n$ and on its least prime divisor, when $G$ belongs to some classes of non-cyclic groups.

9 pages. To appear in Journal of Algebraic Combinatorics