Let \(\gamma_n=[x_1,\dots,x_n]\) be the \(n\)th lower central word. Denote by \(X_n\) the set of \(\gamma_n\)-values in a group \(G\) and suppose that there is a number \(m\) such that \(|g^{X_n}|\leq m\) for each \(g\in G\). We prove that \(\gamma_{n+1}(G)\) has finite \((m,n)\)-bounded order. This generalizes the much celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.