An Application of Cyclotomic Polynomial to Factorization of Abelian Groups

Khalid Amin

doi:10.4236/ojdm.2011.13017

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Open Journal of Discrete Mathematics > Vol.1 No.3, October 2011

An Application of Cyclotomic Polynomial to Factorization of Abelian Groups ()

Khalid Amin

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···A_i···A_n, G is said to have the Hajos-n-proprty if it follows that one of these subsets, say A_i is periodic, meaning that there exists a nonidentity element g in G such that gA_i = A_i . Using some properties of cyclotomic polynomials, we will show that the cyclic groups of orders p^α and groups of type (p²,q²) and (p^α,p^β) where p and q are distinct primes and α, β integers ≥ 1 have this property.

Keywords

Factorizaaton of Finite Abelian Groups, Hajos Property

Share and Cite:

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.

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