On a variation of Sands' method
A subset A of a finite abelian group G is a Z-set if na\(\in A\) for all a in A and n in Z. Two subsets A and B form a factorization of G if every element of G can be expressed uniquely in the form \(a+b\), where \(a\in A\) and \(b\in B\). A period of a subset A is an element a such that \(a+A=A\). Finally, the group G is said to be ``good'' if, in every factorization, at least one of the factors is periodic. It is Z-good if, in every factorization into Z-sets, at least one of the factors is periodic. \textit{A. D. Sands} [Acta Math. Acad. Sci. Hung. 8, 65-86 (1957; Zbl 0079.033)] has given a method which produces all factorizations of good finite abelian groups. The paper under review studies a variation of this method. It investigates when the factorizations it produces have both factors periodic. It is shown that there are factorizations into periodic sets which cannot be obtained using this method.
scientific article; zbMATH DE number 4061506