Factoring an odd abelian group by lacunary cyclic subsets

• Autorzy: Sándor Szabó
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

factorization of finite abelian groups; periodic subsets; cyclic subsets; lacunary cyclic subsets; Hajós-Rédei theory

Kategorie tematyczne

• 05B45: Tessellation and tiling problems
• 68R05: Combinatorics
• 52C22: Tilings in n dimensions
• 20K01: Finite abelian groups [For sumsets, see and ]

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2010
• Tom: 30
• Numer: 2
• Strony: 137-146

Daty

wydano

2010

otrzymano

2008-11-20

poprawiono

2010-01-28

Twórcy

autor

Sándor Szabó

• Institute of Mathematics and Informatics, University of Pécs, Ifjúság u. 6, 7624 Pécs, Hungary

Bibliografia

• [1] K. Corrádi and S. Szabó, A Hajós type result on factoring finite abelian groups by subsets, Mathematica Pannonica 5 (1994), 275-280.
• [2] G. Hajós, Über einfache und mehrfache Bedeckung des n-dimensionalen Raumes mit einem Würfelgitter, Math. Zeit. 47 (1942), 427-467. doi: 10.1007/BF01180974
• [3] 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
• [4] A.D. Sands, A note on distorted cyclic subsets, Mathematica Pannonica 20 (2009), 123-127.
• [5] S. Szabó and A.D. Sands, Factoring Groups into Subsets, Chapman and Hall, CRC, Taylor and Francis Group, Boca Raton 2009.

Identyfikatory

DOI

10.7151/dmgaa.1166