Productivity numbers in paratopological groups

Preserving products in some subcategories of paratopological groups is investigated. N. Noble proved in [6] that a product of sequential topological groups is sequential provided the cardinality of the index set of the product is a non-sequential cardinal. We shall generalize that result not only to paratopological groups but to any bicoreflective subcategory of epireflective subcategories of paratopological groups.