An alternative proof of Hill's criterion of freeness for abelian groups

zbMATH Open1221.20039arXiv1112.0602MaRDI QIDQ5200002

Jorge Eduardo Macías-Díaz

Publication date: 29 July 2011

Abstract: In this note, we provide a different proof of Hill's criterion of freeness for abelian groups. Our proof hinges on the construction of suitable families of subgroups of the links in Hill's theorem and, ultimately, on the construction of such a family of pure subgroups of the group itself.

Full work available at URL: https://arxiv.org/abs/1112.0602

zbMATH Keywords

pure subgroupsfree Abelian groups\(G(\aleph_0)\)-families of subgroupsfreeness criteriaHill criterion

Mathematics Subject Classification ID

Applications of set theory (03E75) Torsion-free groups, infinite rank (20K20) Subgroups of abelian groups (20K27)

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