Dieudonné Completion and PT-Groups

Abstract

We consider the classes of PT-groups, strong PT-groups, completion friendly groups, and Moscow groups introduced by Arhangel’skii for the study of the Dieudonné completion of topological groups. We show that every subgroup H of a Lindelöf P-group is a PT-group, and that H is a strong PT-group iff it is R -factorizable. Assuming CH, we prove that every ω-narrow P-group is a PT-group. Several results regarding products of PT-groups and R -factorizable groups are established as well. We prove that the product of a Lindelöf group and an arbitrary subgroup of a Lindelöf Σ-group is completion friendly, and the same conclusion is valid for the product of an R -factorizable P-group with an almost metrizable group.