CONSTRUCTIONS RELATED TO THE R´EDEI PROPERTY OF GROUPS

We say that a finite abelian group does not have the R´edei property if it can be expressed as a direct product of two of its subsets such that both subsets contain the identity element and both subsets span the whole group. It will be shown that only a small fraction of the finite abelian groups can have the R´edei property. For groups of odd order an explicit list of the possible exceptions is compiled.