Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588604 | Journal of Algebra | 2007 | 9 Pages |
Abstract
It is a well-known homological fact that every Abelian group G has the property that Hom(G,−) commutes with direct products. Here we investigate the ‘dual’ property: an Abelian group G is said to be cosmall if Hom(−,G) commutes with direct products. We show that cosmall groups are cotorsion-free and that no group of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a proper class of strongly compact cardinals, then there are no cosmall groups.
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Physical Sciences and Engineering
Mathematics
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