OJDM  Vol.1 No.3 , October 2011
An Application of Cyclotomic Polynomial to Factorization of Abelian Groups
Abstract: If a finite abelian group G is a direct product of its subsets such that G = A1···Ai···An, G is said to have the Hajos-n-proprty if it follows that one of these subsets, say Ai is periodic, meaning that there exists a nonidentity element g in G such that gAi = Ai . Using some properties of cyclotomic polynomials, we will show that the cyclic groups of orders pα and groups of type (p2,q2) and (pα,pβ) where p and q are distinct primes and α, β integers ≥ 1 have this property.
Cite this paper: nullK. Amin, "An Application of Cyclotomic Polynomial to Factorization of Abelian Groups," Open Journal of Discrete Mathematics, Vol. 1 No. 3, 2011, pp. 136-138. doi: 10.4236/ojdm.2011.13017.

[1]   N. G. De Bruijn, “On the Factorization of Finite Cyclic Groups,” Indagationes Mathematicae, Vol. 15, No.4,

[2]   1953, pp. 370-377.

[3]   G. Hajos, “Uber Einfache und Mehrfaache Bedekung des n-Dimensionales Raumes Mit Einem Wurfelgitter,” Mathematics Zeitschrift, Vol. 47, No. 1, 1942, pp. 427-467. doi:10.1007/BF01180974

[4]   H. Minkowski, “Diophantische Approximationen,” Teuner, Leipzig, 1907.

[5]   L. Redei, “Ein Beitrag Zum Problem Der Faktorisation Von Endlichen Abelschen Gruppen,” Acta Mathematics Hungarica, Vol. 1, No. 2-4, 1950, pp. 197-207. doi:10.1007/BF02021312

[6]   A. Sands, “Factorization of Finite Abelian Groups,” Acta Mathematics Hungarica, Vol. 13, No. 1-2, 1962, pp. 153- 169. doi:10.1007/BF02033634