International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 597-604
doi:10.1155/S0161171286000753

On a variation of Sands' method

Abstract

A subset of a finite additive abelian group G is a Z-set if for all a∈G, na∈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.