  Two string links are equivalent up to $2n$-moves and link-homotopy if and
only if their all Milnor link-homotopy invariants are congruent modulo $n$.
Moreover, the set of the equivalence classes forms a finite group generated by
elements of order $n$. The classification induces that if two string links are
equivalent up to $2n$-moves for every $n>0$, then they are link-homotopic.
