On strongly sum-free subsets of abelian groups

Łuczak, Tomasz; Schoen, Tomasz

Colloquium Mathematicae, Tome 70 (1996), p. 149-151 / Harvested from The Polish Digital Mathematics Library

Résumé

In his book on unsolved problems in number theory [1] R. K. Guy asks whether for every natural l there exists $n_{0} = n_{0} (l)$ with the following property: for every $n \geq n_{0}$ and any n elements $a_{1}, . . ., a_{n}$ of a group such that the product of any two of them is different from the unit element of the group, there exist l of the $a_{i}$ such that $a_{i_{j}} a_{i_{k}} \neq a_{m}$ for $1 \leq j < k \leq l$ and $1 \leq m \leq n$ . In this note we answer this question in the affirmative in the first non-trivial case when l=3 and the group is abelian, proving the following result.

Publié le : 1996-01-01

Zbl 0856.05097

EUDML-ID : urn:eudml:doc:210420

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     author = {Tomasz \L uczak and Tomasz Schoen},
     title = {On strongly sum-free subsets of abelian groups},
     journal = {Colloquium Mathematicae},
     volume = {70},
     year = {1996},
     pages = {149-151},
     zbl = {0856.05097},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv71i1p149bwm}
}

Łuczak, Tomasz; Schoen, Tomasz. On strongly sum-free subsets of abelian groups. Colloquium Mathematicae, Tome 70 (1996) pp. 149-151. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv71i1p149bwm/

Bibliographie

[000] [1] R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, 1994, Problem C14. | Zbl 0805.11001