Strong realcompactness and strong Dieudonné completeness in topological groups

We show that a topological group G is topologically isomorphic to a closed subgroup of a topological product of metrizable groups if and only if G is ω-balanced and G δ -closed in ρG, the Raĭkov completion of G. Then we deduce that a topological group G is topologically isomorphic to a closed subgroup of a topological product of second countable groups if and only if G is ω-narrow and G δ -closed in ρG. pplications of these results to PT-groups and R -factorizable groups are also given.