  We give conditions on the subgroups of the circle to be realized as the
subgroups of eigenvalues of minimal Cantor systems belonging to a determined
strong orbit equivalence class. Actually, the additive group of continuous
eigenvalues E(X,T) of the minimal Cantor system (X,T) is a subgroup of the
intersection I(X,T) of all the images of the dimension group by its traces. We
show, whenever the infinitesimal subgroup of the dimension group associated to
(X,T) is trivial, the quotient group I(X,T)/E(X,T) is torsion free. We give
examples with non trivial infinitesimal subgroups where this property fails. We
also provide some realization results.
