Rédei's theorem

Rédei's theorem

In Group Theory, Rédei's theorem states that "If a finite abelian group is expressed as the product of subsets each of which has a prime number of elements and contains the identity element, then at least one of the factors is a subgroup." This theorem was proved by L. Rédei in 1965.

Formal statement

In any normed factorization of a finite abelian group by subsets of prime cardinality, at least one of the factors is a subgroup.

References

*"A New Proof of Rédei's Theorem" Keresztély Corrádi AND Sándor Szabó Pacific Journal of Mathematics Vol. 140, No. 1, 1989 [http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.pjm/1102647249]
* L. Rédei, Die neue Theorie der endlichen abelschen Gruppen und Verallgemeinerung des Hauptsatzes von Hajόs, Acta Math. Acad. Sci. Hung., 16 (1965), 329-373.


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