On a variation of Sands' method
type: Item
instance of: scholarly article
title: On a variation of Sands' method
zbMATH Open document ID: 0651.20034
DOI: 10.1155/S0161171286000753
author: Evelyn E. Obaid
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46294
review text: 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.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 20K25
zbMATH DE Number: 4061506
zbMATH Keywords: period
zbMATH Keywords: Z-sets
zbMATH Keywords: factorizations
zbMATH Keywords: good finite abelian groups
zbMATH Keywords: periodic sets
MaRDI profile type: Publication
OpenAlex ID: W2011335212
description: scientific article; zbMATH DE number 4061506