Complete decompositions of Abelian groups

Chin, Angelina Yan Mui and Wang, K. L. and Wong, Kok Bin (2021) Complete decompositions of Abelian groups. Communications In Algebra, 49 (7). pp. 2829-2836. ISSN 0092-7872, DOI

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Let G be an abelian group and A(1),..., A(k) (k >= 2) be nonempty subsets of G. The sets A1,..., A(k) are said to form a complete decomposition of G of order k if G = A(1) + ... + A(k) and A(1),..., A(k) are pairwise disjoint. In this paper, we prove the existence of complete decompositions of abelian groups that have at least six elements. We also characterize abelian groups that have a complete decomposition of order two and establish a best upper bound for the order of a complete decomposition of a finite abelian group. For an infinite abelian group, we show the existence of complete decompositions of order k for all k >= 3.

Item Type: Article
Funders: Fundamental Research Grant Scheme (FRGS) [FRGS/1/2019/STG06/UM/02/10]
Uncontrolled Keywords: Abelian group; Complete decomposition; Group factorization
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science
Depositing User: Ms Zaharah Ramly
Date Deposited: 01 Apr 2022 08:54
Last Modified: 01 Apr 2022 08:54

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