Let G be a finite additive abelian group, and suppose that A and B are subsets of G. We say that G = A(&B if every element ge G can be uniquely written in the form g = a + b, where aeA, beB. The study of such decompositions (usually called factorizations in the literature) was initiated by G. Hajos [3] in connection with his solution to a problem of Minkowski in the geometry of numbers.
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