An Elementary Proof That Finite Groups Lack Unique Product Structures Original Research Article

A groupGis said to have a uniquem-element product structure if there is a subsetSofGsuch that the product map φ:Sm→Gis a bijection. D. Dimovski (1992,J. Algebra146, 205–209) proved using character theory that no nontrivial finite group has a uniquem-element product structure formgreater-or-equal, slanted2. We provide an elementary proof of this fact.