On Cosmall Abelian Groups

Authors

Brendan Goldsmith, Technological University DublinFollow
O. Kolman, Universite de Caen

Document Type

Article

Rights

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

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

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.

DOI

https://doi.org/10.1016/j.jalgebra.2007.05.009

Recommended Citation

Goldsmith, B. & Kolman, O. (2007). On Cosmall Abelian Groups. Journal of Algebra, vol. 317, no. 2, pg. 510-518. doi:10.1016/j.jalgebra.2007.05.009