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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