Some density results involving the average order of a finite group

Let o(G) be the average of element orders a finite group G. A research topic concerning this quantity is understanding relation between and o(H), where H subgroup N class nilpotent groups let L(G) lattice In paper, we show that set {o(G)o(H) | G∈N,H∈L(G)} dense in [0,∞). Other density results are outlined throughout paper.