  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.
