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.

## 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.

Item Type: | Article |
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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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