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تسجيل مستخدم جديدOn the structure of zero-sum free set with minimum subset sums in abelian groups
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Let $G$ be an additive abelian group and $Ssubset G$ a subset. Let $Sigma(S)$ denote the set of group elements which can be expressed as a sum of a nonempty subset of $S$. We say $S$ is zero-sum free if $0 otin Sigma(S)$. It was conjectured by R.B.~Eggleton and P.~Erd{o}s in 1972 and proved by W.~Gao et. al. in 2008 that $|Sigma(S)|geq 19$ provided that $S$ is a zero-sum free subset of an abelian group $G$ with $|S|=6$. In this paper, we determined the structure of zero-sum free set $S$ where $|S|=6$ and $|Sigma(S)|=19$.
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