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.”

Keywords

• finite abelian group
• factorization
• Z-set
• good group
• bad group.