On the cyclic 3-manifold covers of the type surface x R

This article contains a proof of the fact that, under certain mild technical conditions, the action of the automorphism group of a cyclic 3-manifold cover of the type SxR, where S is a compact surface, yields a compact quotient. This result is then immediately applied to extend a theorem on the fiberings over the circle of certain compact 3-manifolds which are torus sums. As a corollary, I prove the validity of the conditional main theorem in my article titled "A fibering theorem for 3-manifolds", which appeared in the Journal of Groups, Complexity, Cryptology in 2021 and its subsequent erratum. This paper also furnishes a proof of the irreducibility of the summands of compact 3-manifolds which are torus sums and irreducible.