Manifolds with finite cyclic fundamental groups and codimension 2 fibrators

A closed connected n-manifold N is called a codimension 2 fibrator (codimension 2 orientable fibrator, respectively) if each proper map p:M→B on an (orientable, respectively) (n+2)-manifold M each fiber of which is shape equivalent to N is an approximate fibration. Let r be a nonnegative integer and let N be a closed n-manifold whose fundamental group is isomorphic to H1×H2, where H1 is a group whose order is odd and H2 is a finite direct product of cyclic groups of order 2r. Let q1:N1→N be the covering associated with H1. The main purpose of this paper shows that if N1 is a codimension 2 orientable fibrator, then N is a codimension 2 fibrator.