TITLE:
An Application of Cyclotomic Polynomial to Factorization of Abelian Groups
AUTHORS:
Khalid Amin
KEYWORDS:
Factorizaaton of Finite Abelian Groups, Hajos Property
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.1 No.3,
October
17,
2011
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.