On some series of a group related to the non-abelian tensor square of groups

Let G be a group. We denote by ν(G) certain extension of the non-abelian tensor square G⊗G G×G. In this paper we prove that derived subgroup ν(G)′ is central product three normal subgroups ν(G), all isomorphic to G⊗G. As consequence, describe structure each term and lower series group ν(G).