# Factoring an odd abelian group by lacunary cyclic subsets

Discussiones Mathematicae - General Algebra and Applications (2010)

- Volume: 30, Issue: 2, page 137-146
- ISSN: 1509-9415

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topSándor Szabó. "Factoring an odd abelian group by lacunary cyclic subsets." Discussiones Mathematicae - General Algebra and Applications 30.2 (2010): 137-146. <http://eudml.org/doc/276458>.

@article{SándorSzabó2010,

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.},

author = {Sándor Szabó},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {factorization of finite abelian groups; periodic subsets; cyclic subsets; lacunary cyclic subsets; Hajós-Rédei theory; factorizations of finite Abelian groups},

language = {eng},

number = {2},

pages = {137-146},

title = {Factoring an odd abelian group by lacunary cyclic subsets},

url = {http://eudml.org/doc/276458},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Sándor Szabó

TI - Factoring an odd abelian group by lacunary cyclic subsets

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2010

VL - 30

IS - 2

SP - 137

EP - 146

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/276458

ER -

## References

top- [1] K. Corrádi and S. Szabó, A Hajós type result on factoring finite abelian groups by subsets, Mathematica Pannonica 5 (1994), 275-280. Zbl0831.20069
- [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 Zbl0025.25401
- [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 Zbl0138.26001
- [4] A.D. Sands, A note on distorted cyclic subsets, Mathematica Pannonica 20 (2009), 123-127. Zbl1249.20049
- [5] S. Szabó and A.D. Sands, Factoring Groups into Subsets, Chapman and Hall, CRC, Taylor and Francis Group, Boca Raton 2009. Zbl1167.20030