  In the present paper we give a proof of the fact that the sub-Riemannian cut
locus of a wide class of nilpotent groups of step two, called $H$-type groups,
starting from the origin corresponds to the center of the group. We obtain this
result by completely describing the sub-Riemannian geodesics in the group, and
using these to obtain three disjoint sets of points in the group determined by
the number of geodesics joining them to the origin.
