**
Beiträge zur Algebra und Geometrie **

Contributions to Algebra and Geometry

38(2), 241-248 (1997)

#
An Axiomatic Approach for the Hajós Theorem

##
Keresztély Corrádi, Sándor Szabó

Department of Computer Sciences, Eötvös University Budapest

H--1088 Budapest, Hungary

e-mail: kcorradi@ludens.elte.hu Department of Mathematics, University of Bahrain

P. O. Box 32038 Isa Town, State of Bahrain

e-mail: es050@isa.cc.uob.bh

**Abstract:** Hajós' theorem asserts that if a finite abelian group is a direct product of cyclic subsets, then in fact at least one of the factors must be a subgroup of the group. A cyclic subset is the ``front end'' of a cyclic subgroup. We replace the cyclicity of the factors by an abstract $P$ property in Hajós' theorem for finite abelian groups whose $2$-component is cyclic.

**Keywords:** factorization of finite abelian groups, Hajós-Rédei theory

**Classification (MSC91):** 20K01, 52C22

**Full text of the article:**

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