  The commutator calculus is one of the basic tools in group theory. However,
its extension to the non-associative context, based on the usual definition of
the lower central series of a loop, is not entirely satisfactory. Namely, the
graded abelian group associated to the lower central series of a loop is not
known to carry any interesting algebraic structure. In this note we construct a
new generalization of the lower central series to arbitrary loops that is
tailored to produce a set of multilinear operations on the associated graded
group.
