On Coleman automorphisms of wreath products of finite nilpotent groups by abelian groups

Abstract

Let G = NwrA be a wreath product of a finite nilpotent group N by an abelian group A. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for G. KeywordsColeman automorphisms, wreath products, the normalizer problem MSC(2000): 20C05, 16S34, 20C10Citation: Hai J K, Li Z X. On Coleman automorphisms of wreath products of finite nilpotent groups by abelian groups.