Pure-homogeneous Abelian groups
arXiv:2607.11525
summary
The paper investigates Fraïssé classes of Abelian groups under pure embeddings and characterizes the groups that are universal and homogeneous for several classes, including finitely co‑generated groups, finite groups, and groups of size below a strongly inaccessible cardinal.
Abstract
We study Fraïssé classes of Abelian groups with pure embeddings. We characterize Abelian groups that are universal and homogeneous for: finitely co-generated groups, finite groups, groups of size less that , where is strongly inaccessible.
submitted to Algebra Universalis
Topics & keywords
#abelian groups#pure embeddings#fraïssé classes#universal homogeneous groups#inaccessible cardinalspure embeddingFraïssé limituniversal homogeneousfinite abelian groupsstrongly inaccessible