  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.
