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
Department of Mathematics and Computer Science, San Jose State University, San Jose 95192, California, USA
Received 15 January 1985; Revised 20 March 1986
Copyright © 1986 Evelyn E. Obaid. 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.
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.