The normalizer of a metabelian group in its integral group ring

In this paper, we discuss two cases where all C-automorphisms are inner; therefore, the normalizer property holds for those cases. Our results generalize a result of Marciniak and Roggenkamp. As an application of our theorems, we prove that the normalizer property holds for the integral group ring of a split finite metabelian group with a dihedral Sylow 2-subgroup. Our proofs rely heavily on the method of Marciniak and Roggenkamp.