Outer automorphisms of groups
type: Item
instance of: scholarly article
title: Outer automorphisms of groups
zbMATH Open document ID: 0693.20033
author: Manfred Dugas
author: Rüdiger Göbel
published in: Illinois Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Let \(\kappa\) be a cardinal and H, B groups of cardinality \(\leq \kappa\). If \(\kappa^{\aleph_ 0}=\kappa\), then we construct a group G of cardinality \(\kappa^+\) such that B is contained in G and equals its own normalizer in G. Moreover Aut G\(=H.Inn G\), a semidirect product, and H operates trivially on B. We use transfinite chains of iterated wreath products and rigid systems of torsion-free abelian groups to construct G.
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20K20
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 4134317
zbMATH Keywords: inner automorphisms
zbMATH Keywords: complete groups
zbMATH Keywords: semidirect product
zbMATH Keywords: wreath products
zbMATH Keywords: rigid systems of torsion-free abelian groups
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4134317