On a covering group theorem and its applications

Let p: X → G be an n-fold covering of a compact group G by a connected topological space X. Then there exists a group structure in X turning p into a homomorphism between compact groups. As an application, we describe all n-fold coverings of a compact connected abelian group. Also, a criterion of triviality for n-fold coverings in terms of the dual group and the one-dimensional Čech cohomology group is obtained.