  In Carnot-Caratheodory or sub-Riemannian geometry, one of the major open
problems is whether the conclusions of Sard's theorem holds for the endpoint
map, a canonical map from an infinite-dimensional path space to the underlying
finite-dimensional manifold. The set of critical values for the endpoint map is
also known as abnormal set, being the set of endpoints of abnormal extremals
leaving the base point. We prove that a strong version of Sard's property holds
for all step-2 Carnot groups and several other classes of Lie groups endowed
with left-invariant distributions. Namely, we prove that the abnormal set lies
in a proper analytic subvariety. In doing so we examine several
characterizations of the abnormal set in the case of Lie groups.
