Abstract. Suppose that whenever a finite abelian group $G$ is a direct product of simulated subsets and one other subset then one of these factors must be periodic. In this paper we describe completely the class of all such finite abelian groups $G$. We then consider the same problem when cyclic subsets are admitted as well as simulated subsets. Once again a complete classification is presented.

AMS Subject Classification (1991): 20K01, 11B13

Keyword(s): factorization, Abelian group, simulated subset

Received February 2, 2009, and in revised form April 12, 2010. (Registered under 17/2009.)