ArticleOriginal scientific text
Title
Factoring an odd abelian group by lacunary cyclic subsets
Authors 1
Affiliations
- Institute of Mathematics and Informatics, University of Pécs, Ifjúság u. 6, 7624 Pécs, Hungary
Abstract
It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.
Keywords
factorization of finite abelian groups, periodic subsets, cyclic subsets, lacunary cyclic subsets, Hajós-Rédei theory
Bibliography
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- G. Hajós, Über einfache und mehrfache Bedeckung des n-dimensionalen Raumes mit einem Würfelgitter, Math. Zeit. 47 (1942), 427-467. doi: 10.1007/BF01180974
- L. Rédei, Die neue Theorie der Endlichen Abelschen Gruppen und Verallgemeinerung des Hauptsatzes von Hajós, Acta Math. Acad. Sci. Hungar. 16 (1965), 329-373. doi: 10.1007/BF01904843
- A.D. Sands, A note on distorted cyclic subsets, Mathematica Pannonica 20 (2009), 123-127.
- S. Szabó and A.D. Sands, Factoring Groups into Subsets, Chapman and Hall, CRC, Taylor and Francis Group, Boca Raton 2009.
Pages:
137-146
Main language of publication
English
Received
2008-11-20
Accepted
2010-01-28
Published
2010
DOI: 10.7151/dmgaa.1166
Exact and natural sciences