Disjoint Non-Free Subgoups of Abelian Groups

Details Disjoint Non-Free Subgoups of Abelian Groups Disjoint Non-Free Subgoups of Abelian Groups

2005-09-18

arxiv.org/abs/math/0509406v1

Mathematics

Logic

Scientific paper

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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