Complete ω-balancedness in semitopological groups

We introduce the notion of completely ω-balanced semitopological group and prove that this property is preserved under subgroups and topological products. We also show that a regular semitopological group G admits a homeomorphic embedding as a subgroup into a product of strongly metrizable semitopological groups if and only if G is completely ω-balanced and Ir(G)≤ω.