On the average order of a finite group

Let o(G) be the average order of a finite group G. We show that if o(G)<c, where c∈{136,114}, then G is an elementary abelian 2-group or solvable group, respectively. Also, we prove set containing orders all groups not dense in [a,∞), for a∈[0,136]. also outline some results related to integer values order. Since element popular research topic, pose open problems concerning throughout paper.