The power graph of a torsion-free group of nilpotency class 2

The directed power graph $$\vec {\mathcal {G}}( G)$$ of a group G is the simple digraph with vertex set in which $$x\rightarrow y$$ if y x, and underlying $$\mathcal {G}( . In this paper, three versions definition are discussed, it proved that by any determines other two up to isomorphism. It also torsion-free nilpotency class 2 H such H)\cong \mathcal , then have isomorphic graphs, was an open problem proposed Cameron, Guerra Jurina [9].