boundedly finite conjugacy classes of tensors

Let n be a positive integer and let g be a group. we denote by ν(g) a certain extension of the non-abelian tensor square g ⊗ g by g × g. set t⊗(g) = {g ⊗ h | g, h ∈ g}. we prove that if the size of the conjugacy class x^ν(g) ≤ n for every x ∈ t⊗(g), then the second derived subgroup ν(g) ′′ is finite with n-bounded order. moreover, we obtain a sufficient condition for a group to be a bfc-group.