Sum-full sets are not zero-sum-free

Sum-full sets are not zero-sum-free

Let A be a finite, nonempty subset of an abelian group. We show that if every element of A is a sum of two other elements, then A has a nonempty zero-sum subset. That is, a (finite, nonempty) sum-full subset of an abelian group is not zero-sum-free.

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Bibliographische Detailangaben
Veröffentlicht in:Linear algebra and its applications 2021-09, Vol.625, p.241-247
Hauptverfasser: Lev, Vsevolod F., Nagy, János, Pach, Péter Pál
Format: Artikel
Sprache:eng
Schlagworte:
Group theory
Linear algebra
Sum-full sets
Zero-sum sets
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Beschreibung
Zusammenfassung:Let A be a finite, nonempty subset of an abelian group. We show that if every element of A is a sum of two other elements, then A has a nonempty zero-sum subset. That is, a (finite, nonempty) sum-full subset of an abelian group is not zero-sum-free.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.05.008