  Dimension groups are complete invariants of strong orbit equivalence for
minimal Cantor systems. This paper studies a natural family of minimal Cantor
systems having a finitely generated dimension group, namely the primitive
unimodular proper S-adic subshifts. They are generated by iterating sequences
of substitutions. Proper substitutions are such that the images of letters
start with a same letter, and similarly end with a same letter. This family
includes various classes of subshifts such as Brun subshifts or dendric
subshifts, that in turn include Arnoux-Rauzy subshifts and natural coding of
interval exchange transformations. We compute their dimension group and
investigate the relation between the triviality of the infinitesimal subgroup
and rational independence of letter measures. We also introduce the notion of
balanced functions and provide a topological characterization of bal-ancedness
for primitive unimodular proper S-adic subshifts.
