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On subset sums of a zero-sum free set ofseven elements from an abelian group

Volume 160 / 2020

Jiangtao Peng, Wanzhen Hui, Feng Lv Colloquium Mathematicum 160 (2020), 1-14 MSC: Primary 11B75; Secondary 11P70. DOI: 10.4064/cm7580-3-2019 Published online: 21 January 2020

Abstract

Let $G$ be a finite abelian group and $S\subset G$. Let $\Sigma (S)$ denote the set of group elements which can be expressed as a sum of a nonempty subset of $S$. We say that $S$ is zero-sum free if $0\notin \Sigma (S)$. Suppose $S$ is zero-sum free with $|S|=7$. It was proved by P. Yuan and X. Zeng in 2010 that $|\Sigma (S)|\geq 24$. We show that if $\langle S\rangle $ is not cyclic, then $|\Sigma (S)|\geq 25$. Furthermore if $|\Sigma (S)|= 24$ then $\langle S\rangle $ is a cyclic group and $25 \,|\, |G|$, which supports a conjecture of R. B. Eggleton and P. Erdős.

Authors

  • Jiangtao PengCollege of Science
    Civil Aviation University of China
    Tianjin 300300, P.R. China
    e-mail
  • Wanzhen HuiCollege of Science
    Civil Aviation University of China
    Tianjin 300300, P.R. China
    e-mail
  • Feng LvCollege of Aeronautical Engineering
    Civil Aviation University of China
    Tianjin 300300, P.R. China
    e-mail

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