An Application of Cyclotomic Polynomial to Factorization of Abelian Groups

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DOI: 10.4236/ojdm.2011.13017   PDF   HTML     4,374 Downloads   8,119 Views  

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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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