Productivity of sequences in non-abelian topological groups

In [2] various natural generalizations of the classical concepts of “convergent series”, “unconditionally convergent series” and “absolutely convergent series” were thoroughly studied in the realm of topological groups. Nevertheless, some natural questions posed in [2] that have answers for abelian topological groups remained open in the realm of non-abelian topological groups. In our paper we provide a general schema for constructing strong counterexamples that answers many of those questions in negative.