Complete decompositions of Abelian groups
Document Type
Article
Publication Date
6-18-2021
Abstract
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.
Keywords
Abelian group, Complete decomposition, Group factorization
Divisions
Science
Funders
Fundamental Research Grant Scheme (FRGS) [FRGS/1/2019/STG06/UM/02/10]
Publication Title
Communications In Algebra
Volume
49
Issue
7
Publisher
Taylor & Francis Inc
Publisher Location
530 WALNUT STREET, STE 850, PHILADELPHIA, PA 19106 USA