  In the first part, we prove that the dominion (in the sense of Isbell) of a
subgroup of a finitely generated nilpotent group is trivial in the category of
all nilpotent groups. In the second part, we show that the dominion of a
subgroup of a finitely generated nilpotent group of class two is trivial in the
category of all metabelian nilpotent groups.
