Geodesic
Factoring an odd abelian group by lacunary cyclic subsets
Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 2, pp. 137-146 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

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 
@article{DMGAA_2010_30_2_a0,
     author = {Szab\'o, S\'andor},
     title = {Factoring an odd abelian group by lacunary cyclic subsets},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {137--146},
     year = {2010},
     volume = {30},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2010_30_2_a0/}
}
TY  - JOUR
AU  - Szabó, Sándor
TI  - Factoring an odd abelian group by lacunary cyclic subsets
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2010
SP  - 137
EP  - 146
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2010_30_2_a0/
LA  - en
ID  - DMGAA_2010_30_2_a0
ER  - 
%0 Journal Article
%A Szabó, Sándor
%T Factoring an odd abelian group by lacunary cyclic subsets
%J Discussiones Mathematicae. General Algebra and Applications
%D 2010
%P 137-146
%V 30
%N 2
%U http://geodesic.mathdoc.fr/item/DMGAA_2010_30_2_a0/
%G en
%F DMGAA_2010_30_2_a0
Szabó, Sándor. Factoring an odd abelian group by lacunary cyclic subsets. Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 2, pp. 137-146. http://geodesic.mathdoc.fr/item/DMGAA_2010_30_2_a0/

[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.