  We study aspherical manifolds that do not support Anosov diffeomorphisms.
Weakening conditions of Gogolev and Lafont, we show that the product of an
infranilmanifold with finitely many aspherical manifolds whose fundamental
groups have trivial center and finite outer automorphism group does not support
Anosov diffeomorphisms. In the course of our study, we obtain a result of
independent group theoretic and topological interest on the stability of the
Hopf property, namely, that the product of finitely many Hopfian groups with
trivial center is Hopfian.
