  This paper is the third in a series dedicated to the fundamentals of
sub-Riemannian geometry and its implications in Lie groups theory:
"Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at
http://arxiv.org/abs/math.MG/0210189, and "Tangent bundles to sub-Riemannian
groups", math.MG/0307342, available at http://arxiv.org/abs/math.MG/0307342 .
