  A simple Almost-Riemmanian Structure on a Lie group G is defined by a linear
vector field and dim(G)-1 left-invariant ones. We state results about the
singular locus, the abnormal extremals and the desingularization of such ARS's,
and these results are illustrated by examples on the 2D affine and the
Heisenberg groups.These ARS's are extended in two ways to homogeneous spaces,
and a necessary and sufficient condition for an ARS on a manifold to be
equivalent to a general ARS on a homogeneous space is stated.
