A Boolean power and a direct product of abelian groups

Abstract

A group means an abelian group in this paper. A Boolean power and a direct product of groups consist of all global sections of groups in some Boolean extensions $V^{(B)}$ . We shall study about a homomorphism $h$ whose domain $s$ a group consisting of all the global sections of a group in $V^{(B)}$ . We investigate two cases: one of them is that the range of $h$ is a slender group, which is related to a torsion-free group, and the other is that the range of $h$ is an infinite direct sum, which is related to a torsion group. We extend a few theorems which have been obtained in [4] and [5]. As in [5], we not only extend theorems, but improve them and give a good standing point of view.