Finite groups with the same power graph

The power graph P(G) of a group G is with vertex set G, where two vertices u and v are adjacent if only u≠v um=v or vm=u for some positive integer m. In this paper, we raise study the following question: For which natural numbers n every groups order isomorphic graphs isomorphic? particular, it proved that all such odd number cube-free also they not multiples 16 in general. Moreover, show finite have one them nilpotent, same true other one.