Properties of Ext and quasi-splitting of Abelian groups

Abstract

represents an element of finite order in Ext (G/Gt, Gt), where Gt denotes the torsion subgroup of G. This leads to an answer to the question, posed by L. FUCHS at the New Mexico State University Conference on Abelian Groups: I f a group G is quasi-isomorphic to a group which splits over its torsion subgroup, does G necessarily split over its torsion subgroup? z The following notations and conventions will be used. The word group will mean Abelian group. I f G is a group, G t will denote the torsion subgroup of G, G v the p-pr imary component of G t, and G [n] the subgroup of elements x of G such that nx = 0. The identity homomorphism of G will be denoted by i~. I f G t is a summand of G, then G is called a splitting group.