Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 46, No. 1, pp. 119123 (2005) 

Hajós' theorem and the partition lemmaSándor SzabóDepartment of Mathematics, University of Bahrain, P. O. Box 32038, State of BahrainAbstract: If a finite abelian group is a direct product of cyclic subsets, then at least one of the factors must be a subgroup. This result is due to G. Hajós. The purpose of this paper is to show that Hajós' theorem can be proved using the socalled partition lemma. Keywords: factorization of finite abelian groups, HajósRédei theory Classification (MSC2000): 20K01 52C22; 52C22 Full text of the article:
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