Finite groups with integer harmonic mean of element orders (Q6669420)

Let \(G\) be a finite group, \(g \in G\) and let \(o(g)\) be the order of \(g\).\N\NIn this paper, the authors define the harmonic mean of element orders of \(G\) as \(h_{m}(G)= \big | G \big | \cdot \big (\sum_{g \in G} o(g)^{-1} \big)^{-1}\). They present a series of properties for this function, and then they study groups \(G\) for which \(h_{m}(G)\) is an integer.