Dieudonné Completion and PT-Groups

摘要

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 Lindel?f P -group is a PT -group, and that H is a strong PT -group iff it is ?-factorizable. Assuming CH, we prove that every ω -narrow P -group is a PT -group. Several results regarding products of PT -groups and ?-factorizable groups are established as well. We prove that the product of a Lindel?f group and an arbitrary subgroup of a Lindel?f Σ-group is completion friendly, and the same conclusion is valid for the product of an ?-factorizable P -group with an almost metrizable group.