A GENERALIZED FORM OF HAJOS THEOREM

Hajos proved that if a finite abelian group is a direct product of cyc lic subsets, then at least one of the factors is a subgroup of the gro up. A cyclic subset consists of the ''first some consecutive elements' ' of a cyclic subgroup. We give a generalization for Hajos' theorem. T he proof of this generalization is simpler and the steps are better mo tivated than the proof of the original result.