A. Storozhev, INFINITE CYCLIC VERBAL SUBGROUPS OF RELATIVELY FREE GROUPS, Proceedings of the American Mathematical Society, 124(10), 1996, pp. 2953-2954
We prove that there exist a relatively free group H and a word w(z, y)
in two variables such that the verbal subgroup of H defined by w(x, y
) is an infinite cyclic group whereas w(z, y) has only one nontrivial
value in H.