Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
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.
Recommended Citation
Goldsmith, Brendan and Kolman, O., "On cosmall Abelian groups" (2007). Articles. Paper 40.
http://arrow.dit.ie/scschmatart/40
Publication Details
In Journal of Algebrar, Vol. 317, (2007), pp.510-518. http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WH2-4NS2GMW-3-5&_cdi=6838&_user=2322584&_orig=browse&_coverDate=11%2F15%2F2007&_sk=996829997&view=c&wchp=dGLzVzz-zSkWA&md5=5672ace58e6d7dc79674be29544ec7c8&ie=/sdarticle.pdf