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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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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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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.


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