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An Application of Cyclotomic Polynomial to Factorization of Abelian Groups

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DOI: 10.4236/ojdm.2011.13017    4,159 Downloads   7,897 Views  
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

K. 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.

References

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[4] H. Minkowski, “Diophantische Approximationen,” Teuner, Leipzig, 1907.
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[6] A. Sands, “Factorization of Finite Abelian Groups,” Acta Mathematics Hungarica, Vol. 13, No. 1-2, 1962, pp. 153- 169. doi:10.1007/BF02033634

  
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