On a variation of Sands' method

Evelyn E. Obaid

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-8

Abstract:

A subset of a finite additive abelian group G is a Z -set if for all a ∈ G , n a ∈ G for all n ∈ Z . The group G is called Z-good if in every factorization G = A ⊕ B , where A and B are Z -sets at least one factor is periodic. Otherwise G is called Z -bad.

The purpose of this paper is to investigate factorizations of finite ablian groups which arise from a variation of Sands' method. A necessary condition is given for a factorization G = A ⊕ B , where A and B are Z -sets, to be obtained by this variation. An example is provided to show that this condition is not sufficient. It is also shown that in general all factorizations G = A ⊕ B , where A and B are Z -sets, of a Z -good group do not arise from this variation of Sands' method.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:806218

DOI: 10.1155/S0161171286000753

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