  We use the theory of dual of Fr\'echet-Schwartz (DFS) spaces to establish a
sufficient condition for top-degree solvability for the differential complex
associated to a hypocomplex locally integrable structure. As an application, we
show that the top-degree cohomology of left-invariant hypocomplex structures on
a compact Lie group can be computed only by using left-invariant forms, thus
reducing the computation to a purely algebraic one. In the case of
left-invariant elliptic involutive structures on compact Lie groups, under
certain reasonable conditions, we prove that the cohomology associated to the
involutive structure can be computed only by using left-invariant forms.
