This project is concerned with the relationship between the torsion product and various classes of abelian p-groups. Let C be a class of abelian groups such as the class of all totally projective abelian p-groups and let A,B be abelian groups in C. The principal investigator will describe Tor(A,B); determine if Tor(A,B) is in C; and characterize C using the torsion product. This project is in the general area of abelian group theory. Finite abelian groups have been completely classified but the classification of infinite abelian groups remains elusive. This research will contribute to the knowlege of infinite abelian groups by studying the interplay between set theory and abelian groups.
