Disjoint Non-Free Subgoups of Abelian Groups

Andreas Blass; Saharon Shelah

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arXiv · math/0509406

Disjoint Non-Free Subgoups of Abelian Groups

Andreas Blass·Saharon Shelah

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Abstract

Let G be an abelian group and let lambda be the smallest rank of any group whose direct sum with a free group is isomorphic to G. If lambda is uncountable, then G has lambda pairwise disjoint, non-free subgroups. There is an example where lambda is countably infinite and G does not have even two disjoint, non-free subgroups.

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BibTeX RIS

Andreas Blass, Saharon Shelah. 2005-09-18. Disjoint Non-Free Subgoups of Abelian Groups. https://arxiv.org/abs/math/0509406

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