  We prove that the relative K-groups associated with a nilpotent extension of
Z/p^N Z-algebras and the bi-relative K-groups associated with a Milnor square
of Z/p^N Z-algebras are p-primary torsion groups of bounded exponent. We also
show that, in general, the cyclotomic trace map extends from Quillen K-theory
to Bass completed non-connective algebraic K-theory.
