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- W2950330539 abstract "For a group $G$, let $U$ be the group of units of the integral group ring $mathbb{Z}G$. The group $G$ is said to have the normalizer property if $text{N}_U(G)=text{Z}(U)G$. It is shown that Blackburn groups have the normalizer property. These are the groups which have non-normal finite subgroups, with the intersection of all of them being nontrivial. Groups $G$ for which class-preserving automorphisms are inner automorphisms, $text{Out}_c(G)=1$, have the normalizer property. Recently, Herman and Li have shown that $text{Out}_c(G)=1$ for a finite Blackburn group $G$. We show that $text{out}_c(G)=1$ for the members $G$ of a few classes of metabelian groups, from which the Herman--Li result follows. Together with recent work of Hertweck, Iwaki, Jespers and Juriaans, our main result implies that, for an arbitrary group $G$, the group of hypercentral units of $U$ is contained in $text{Z}(U)G$." @default.
- W2950330539 created "2019-06-27" @default.
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- W2950330539 date "2007-01-05" @default.
- W2950330539 modified "2023-09-27" @default.
- W2950330539 title "Class-preserving automorphisms and the normalizer property for Blackburn groups" @default.
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