BOUNDEDLY FINITE CONJUGACY CLASSES OF TENSORS

Let n be a positive integer and let G be a group. We denote by nu(G) a certain extension of the non-abelian tensor square G circle times G by G x G. Set T-circle times(G) = {g circle times h vertical bar g, h is an element of G}. We prove that if the size of the conjugacy class vertical bar x(nu(G))vertical bar <= n for every x is an element of T-circle times(G), then the second derived subgroup nu(G)'' is finite with n-bounded order. Moreover, we obtain a sufficient condition for a group to be a BFC-group.