  The time-dependent density-matrix theory (TDDM) where the
Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for reduced density matrices is
truncated by approximating a three-body density matrix with one-body and
two-body density matrices is applied to the Lipkin model. It is shown that in
the large $N$ limit the ground state in TDDM approaches the exact solution.
Various truncation schemes for the three-body density matrix are also tested
for an extended three-level Lipkin model.
