Complete decompositions of Abelian groups

• Main Authors: Chin, Angelina Yan Mui, Wang, K. L., Wong, Kok Bin
• Format: Article
• Published: Taylor & Francis Inc 2021
• Subjects: QA Mathematics
• Online Access: http://eprints.um.edu.my/26989/
• Institution: Universiti Malaya

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.