The normalizer of a metabelian group in its integral group ring

✍ Scribed by Yuanlin Li

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 102 KB
• Volume: 256
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00102-3

✦ Synopsis

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.