The one-dimensional compact connected abelian groups, called solenoids, are classified and constructed as topological subgroups of the torus Tא0. For an arbitrary solenoid 6 ̸= T, we exhibit a nonsplitting extension of 6 by a profinite group, dual to a nonsplitting extension 0 → tor(A) → A → F → 0 of abelian groups where F is a rank-1 torsion-free group ̸= Z. The constructed groups A are generalizations of examples of Fuchs.
