Outer automorphisms of groups
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.
rigid systems of torsion-free abelian groups
scientific article; zbMATH DE number 4134317