On the size of complete decompositions of finite cyclic groups
Document Type
Article
Publication Date
10-3-2022
Abstract
Let G be an abelian group and A(1), ..., A(k) (k >= 2) be nonempty subsets of G. The sets A(1), ..., A(k) are said to form a complete decomposition of G of order k if G = A(l) + ... + A(k) and A(1), ..., A(k) are pairwise disjoint. The size of a complete decomposition A(1), ..., A(k) of G is defined to be = vertical bar boolean OR(k)(i=1)A(i)vertical bar. = Sigma(k)(i=1) vertical bar A(i)vertical bar. In this paper, we determine the minimum and maximum size of a complete decomposition of a finite cyclic group.
Keywords
Abelian group, Complete decomposition, Cyclic group
Divisions
MathematicalSciences
Funders
Fundamental Research Grant Scheme (FRGS) (Grant No: FRGS/1/2019/STG06/UM/02/10)
Publication Title
Communications In Algebra
Volume
50
Issue
10
Publisher
Taylor & Francis Inc
Publisher Location
530 WALNUT STREET, STE 850, PHILADELPHIA, PA 19106 USA