A Note on the Nilpotent Topological Groups of Class at Most Two and the Set of Bilinear Mappings

Division of the set of all groups into families provides a convenient method of classifying groups. In this paper, we show that there is a one to one correspondence between the set of nilpotent topological groups of class at most two and the set of continuous regular bilinear mappings. It is known that there is a relation between the second cohomology of a topological group with trivial coefficient and the group of central extensions. As a result, every nilpotent group of class two may be embedded in a central extension of abelian groups with bilinear cocycle.