We prove, under certain conditions, that if a solenoidal group (i.e. 1-dimensional compact connected abelian group) acts effectively on a compact space then the fixed point set is nonempty and H∗ G(X, Q) has a presentation similar to the presentation of H∗ (X, Q) as proven by Chang in the case of a circle group. We prove, under certain conditions, that if a solenoidal group (i.e. 1-dimensional compact connected abelian group) acts effectively on a compact space then the fixed point set is nonempty and H∗ G(X, Q) has a presentation similar to the presentation of H∗ (X, Q) as proven by Chang in the case of a circle group.