  We prove the smoothness of abnormal minimizers of subriemannian manifolds of
step 3 with a nilpotent basis. We prove that rank 2 Carnot groups of step 4
admit no strictly abnormal minimizers. For any subriemannian manifolds of step
less than 7, we show all abnormal minimizers have no corner type singularities,
which partly generalize the main result of Leonardi-Monti.
