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

Department of Mathematics, University of Bahrain
P. O. Box 32038 Isa Town, State of Bahrain

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

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