Twisted Alexander polynomials and surjectivity of a group homomorphism
  If phi: G-->G' is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G'. As an application, we show non-existence of surjective homomorphism between certain knot groups. 
Teruaki Kitano, Masaaki Suzuki and Masaaki Wada