Partial Decomposition Bases and Global Warfield Groups |
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Authors: | Carol Jacoby |
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Institution: | Jacoby Consulting, Long Beach, California, USA |
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Abstract: | The class of abelian groups with partial decomposition bases was developed by the first author in order to generalize Barwise and Eklof's classification of torsion groups in L∞ω. In this article, we continue to explore algebraic characteristics of this class and establish a uniqueness theorem, extending our previous work on mixed p-local groups to the global case. It is shown that groups with partial decomposition bases are characterized in terms of Warfield groups and k-groups of Hill and Megibben. In fact, we prove that the class of groups with partial decomposition bases is identical to the class of k-groups, and, as such, closed under direct summands, and that every finitely generated subgroup of a k-group is locally nice. Also, we introduce and explore subgroups possessing a partial subbasis. As an application, it is shown that isotype k-subgroups of abelian groups are k-groups. |
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Keywords: | *-Decomposition set k-Group k-Subgroup Moore group Partial decomposition basis Partial subbasis Partial isomorphism Warfield group |
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