Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
1.1 MATHEMATICS
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
Recommended Citation
Goldsmith, B., Kolman, O. (2007). On cosmall Abelian Groups. Journal of Algebra, 317, pp.510-518 doi:10.1016/j.jalgebra.2007.05.009
Publication Details
Journal of Algebra