# On strongly sum-free subsets of abelian groups

Colloquium Mathematicae (1996)

- Volume: 71, Issue: 1, page 149-151
- ISSN: 0010-1354

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topŁuczak, Tomasz, and Schoen, Tomasz. "On strongly sum-free subsets of abelian groups." Colloquium Mathematicae 71.1 (1996): 149-151. <http://eudml.org/doc/210420>.

@article{Łuczak1996,

abstract = {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 $n ≥ n_0$ 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 $a_\{i_j\}a_\{i_k\} ≠ a_m$ for $1 ≤ j < k ≤ l$ and $1 ≤ m ≤ n$. 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.},

author = {Łuczak, Tomasz, Schoen, Tomasz},

journal = {Colloquium Mathematicae},

keywords = {sum-free subsets; abelian group},

language = {eng},

number = {1},

pages = {149-151},

title = {On strongly sum-free subsets of abelian groups},

url = {http://eudml.org/doc/210420},

volume = {71},

year = {1996},

}

TY - JOUR

AU - Łuczak, Tomasz

AU - Schoen, Tomasz

TI - On strongly sum-free subsets of abelian groups

JO - Colloquium Mathematicae

PY - 1996

VL - 71

IS - 1

SP - 149

EP - 151

AB - 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 $n ≥ n_0$ 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 $a_{i_j}a_{i_k} ≠ a_m$ for $1 ≤ j < k ≤ l$ and $1 ≤ m ≤ n$. 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.

LA - eng

KW - sum-free subsets; abelian group

UR - http://eudml.org/doc/210420

ER -

## References

top- [1] R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, 1994, Problem C14. Zbl0805.11001

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