Class-preserving automorphisms and the normalizer property for Blackburn groups
| dc.creator | Hertweck, Martin | |
| dc.creator | Jespers, Eric | |
| dc.date | 2007-01-05 | |
| dc.date | 2008-03-07 | |
| dc.date.accessioned | 2026-07-07T09:25:20Z | |
| dc.date.available | 2026-07-07T09:25:20Z | |
| dc.description | 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 $\text{Z}(U)G$. | |
| dc.description | 10 pages. Proof of Lemma 2.2 improved. Added Example 2.3 | |
| dc.identifier | https://arxiv.org/abs/math/0701159 | |
| dc.identifier | http://arxiv.org/abs/math/0701159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156371 | |
| dc.subject | Group Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 20F28; 16S34 | |
| dc.title | Class-preserving automorphisms and the normalizer property for Blackburn groups | |
| dc.type | text |