On the size of complete decompositions of finite cyclic groups

Chin, A. Y. M. and Wang, K. L. and Wong, Kok Bin (2022) On the size of complete decompositions of finite cyclic groups. Communications In Algebra, 50 (10). pp. 4145-4154. ISSN 0092-7872, DOI https://doi.org/10.1080/00927872.2022.2057520.

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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.

Item Type: Article
Funders: Fundamental Research Grant Scheme (FRGS) (Grant No: FRGS/1/2019/STG06/UM/02/10)
Uncontrolled Keywords: Abelian group; Complete decomposition; Cyclic group
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Institute of Mathematical Sciences
Depositing User: Ms. Juhaida Abd Rahim
Date Deposited: 18 Oct 2023 04:43
Last Modified: 18 Oct 2023 04:43
URI: http://eprints.um.edu.my/id/eprint/42021

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