International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 597-604

On a variation of Sands' method

Evelyn E. Obaid

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.


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.