On the capability, non-abelian tensor square and non-commuting graph of prime power groups

In this paper, we give necessary and sufficient conditions under which finite non-abelian metacyclic p-group (p an odd prime) G is capable. We also, determine the non-abelian tensor square G\otimes G for the groups of order p^{\alpha+\beta} for some \alpha, \beta\in \mathbb{N}. Finally, we obtain some conditions on the parameters of two prime power groups G_p and G_q in which the groups have isomorphic non-commuting graphs.

کلیدواژه ها:

Prime power group ، capable group ، tensor square ، isomorphic graphs