A dosed connected n-manifold N is called a codimension-2 fibrator (codimension-2 orientable fibrator, respectively) if every 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. The aim of this paper is to prove the following three statements:
(i) If N is a hopfian manifold with \H-1(N)\ less than or equal to 2, then N is a codimension-2 orientable fibrator.
(ii) If N is a closed manifold whose fundamental group is isomorphic to a finite product of Z(2r)'s for some r, then N is a codimension-2 fibrator.
(iii) Let N be a hopfian n-manifold with H-1 (N) approximate to Z(2). If the commutator subgroup [pi(1)(N), pi(1)(N)] of pi(1)(N) is a hyperhopfian group, then N is a codimension-2 fibrator.
The method used in (i) and (ii) induces the following: If a codimension-2 PL fibrator N satisfies that both pi(1)(N) and pi(k-1)(N) are finite and that pi(i)(N) = 0 for 2 less than or equal to i less than or equal to k - 2, then N is a codimension-k PL fibrator. (C) 2000 Elsevier Science B.V. All rights reserved.