Abstract. Let the finite abelian group $G$ be the direct product of the cyclic subsets $A_1,\ldots,A_n$ with $1\in A_1\cap\ldots \cap A_n$. We prove that every quasi-perodic partial product of this product contains a subgroup among its factors. This extends a result of G. Hajós stating the existence of a subgroup among the factors of the whole product.

AMS Subject Classification (1991): 20K01, 52C22

Keyword(s): factorization of finite abelian groups, Hajós--Rédei theory

Received September 30, 1994. (Registered under 5622/2009.)