International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1986 / Article

Open Access

Volume 9 |Article ID 806218 | https://doi.org/10.1155/S0161171286000753

Evelyn E. Obaid, "On a variation of Sands' method", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 806218, 8 pages, 1986. https://doi.org/10.1155/S0161171286000753

On a variation of Sands' method

Received15 Jan 1985
Revised20 Mar 1986

Abstract

A subset of a finite additive abelian group G is a Z-set if for all aG, naG for all nZ. The group G is called “Z-good” if in every factorization G=AB, 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=AB, 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=AB, where A and B are Z-sets, of a “Z-good” group do not arise from this variation of Sands' method.

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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