The OP subgroup of a torsion-free LCA group

Abstract

Let $G$ be a locally compact abelian (LCA) group. We denote by $G_{op}$, the intersection of all open pure subgroups of $G$, which we call the $OP$ subgroup of $G$. In this paper, we prove that the $OP$ subgroup of a torsion-free LCA group $G$ is a non-zero pure subgroup of $G$.