# On a covering group theorem and its applications

## (*Lobachevskii Journal of Mathematics, Volume X*)

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 Cech cohomology group is obtained.