A Factorization Theorem for Topological Abelian Groups

Using the nice properties of the w-divisible weight and the w-divisible groups, we prove a factorization theorem for compact abelian groups K; namely, K = K _tor  × K _d , where K _tor is a bounded torsion compact abelian group and K _d is a w-divisible compact abelian group. By Pontryagin duality this result is equivalent to the same factorization for discrete abelian groups proved in 9 Galindo , J. , Macario , S. ( 2011 ). Pseudocompact group topologies with no infinite compact subsets . J. Pure and Appl. Algebra 215 : 655 – 663 .Crossref], Web of Science ®] , Google Scholar]].