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factorization of finite abelian groups; periodic subset; cyclic subset; Hajós's theorem
It is proved that if a finite abelian group is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be periodic. This result generalizes Hajós's factorization theorem.
[1] Corrádi K., Szabó S.: A Hajós type result on factoring finite abelian groups by subsets. Math. Pannon. 5 (1994), 275–280. MR 1304856
[2] Hajós G.: Über einfache und mehrfache Bedeckung des $n$-dimensionalen Raumes mit einem Würfelgitter. Math. Z. 47 (1942), 427–467. DOI 10.1007/BF01180974 | MR 0006425
[3] Sands A.D.: A note on distorted cyclic subsets. Math. Pannon. 20 (2009), 123–127. MR 2517716
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