On subset sums of zero-sum free sets of abelian groups-Reference-Cited by-同舟云学术

On subset sums of zero-sum free sets of abelian groups

Published:2019-03-21 Issue:03 Volume:15 Page:645-654
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Peng Jiangtao¹,Hui Wanzhen¹,Li Yuanlin²,Sun Fang¹

Affiliation:

1. College of Science, Civil Aviation University of China, Tianjin, 300300, P. R. China

2. Department of Mathematics and Statistics, Brock University, St. Catharines, Ontario L2S 3A1, Canada

Abstract

Let [Formula: see text] be a finite abelian group and [Formula: see text] be a subset of [Formula: see text]. Let [Formula: see text] denote the set of group elements which can be expressed as a sum of a nonempty subset of [Formula: see text]. We say that [Formula: see text] is zero-sum free if [Formula: see text]. In this paper, we show that if [Formula: see text] is zero-sum free with [Formula: see text], then [Formula: see text]. Furthermore, if [Formula: see text] is zero-sum free and [Formula: see text], with the assumption that the subgroup generated by [Formula: see text] is noncyclic and the order [Formula: see text], we are able to show that [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042119500349

Reference9 articles.

1. Zero-sum free sets with small sum-set

2. Two combinatorial problems in group theory

3. Zero-sum problems in finite abelian groups: A survey

4. Subsums of a Zero-sum Free Subset of an Abelian Group

5. Non-Unique Factorizations

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