An Application of Cyclotomic Polynomial to Factorization of Abelian Groups

• 作者: Khalid Amin
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Factorizaaton of FINITE ABELIAN GROUPS Hajos PROPERTY
• 年，卷（期）: 2011,（3）
• 页码范围: 136-138
• 页数: 3页
• 分类号: O1

摘要

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.