A new proof of Rédei's theorem
Let G be a finite Abelian group written multiplicatively, and let \(A_ 1,...,A_ n\) be subsets of G. If each \(g\in G\) is uniquely expressible in the form \(g=a_ 1...a_ n\), \(a_ 1\in A_ 1,...,a_ n\in A_ n\), then we say that \(G=A_ 1...A_ n\) a factorization of G. If each \(A_ i\) contains the identity element, we speak of a normed factorization. In 1965, L. Rédei proved the followed theorem: in any normed factorization of a finite Abelian group by subsets of prime cardinality, at least one of the factors is a subgroup [see \textit{L. Rédei}, Acta Math. Acad. Sci. Hung. 16, 329-373 (1965; Zbl 0138.260)]. In the present paper, the authors give a shorter proof of Rédei's theorem. One of the authors, \textit{S. Szabó}, gave a stronger form of Rédei's theorem for p-groups [see the preceding review Zbl 0687.20027)].
scientific article; zbMATH DE number 4125679