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Article

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This item is available under a Creative Commons License for non-commercial use only

Disciplines

1.1 MATHMATICS

Publication Details

Journal of Algebra

Abstract

It is a well-known homological fact that every Abelian groupGhas the property that Hom(G,−)com-mutes with direct products. Here we investigate the ‘dual’ property: an Abelian groupGis said to be cosmallif Hom(−,G)commutes with direct products. We show that cosmall groups are cotorsion-free and that nogroup of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a properclass of strongly compact cardinals, then there are no cosmall group

DOI

https://0.1016/j.jalgebra.2007.05.009

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