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

Anosov diffeomorphisms of products II. Aspherical manifolds