Finite sheeted covering maps over 2-dimensional connected, compact Abelian groups

Let G be a 2-dimensional connected, compact Abelian group and s be a positive integer. We prove that a classification of s-sheeted covering maps over G is reduced to a classification of s-index torsionfree supergroups of the Pontrjagin dual . Using group theoretic results from earlier paper we demonstrate its consequences. We also prove that for a connected compact group Y:(1)Every finite-sheeted covering map from a connected space over Y is equivalent to a covering homomorphism from a compact, connected group.(2)If two finite-sheeted covering homomorphisms over Y are equivalent, then they are equivalent as topological homomorphisms.