Geodesic
On strongly sum-free subsets of abelian groups
Colloquium Mathematicum, Tome 71 (1996) no. 1, pp. 149-151.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm-71-1-149-151

Tomasz Łuczak 1 ; Tomasz Schoen 1

1 
@article{10_4064_cm_71_1_149_151,
     author = {Tomasz {\L}uczak and Tomasz Schoen},
     title = {On strongly sum-free subsets of abelian groups},
     journal = {Colloquium Mathematicum},
     pages = {149--151},
     publisher = {mathdoc},
     volume = {71},
     number = {1},
     year = {1996},
     doi = {10.4064/cm-71-1-149-151},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-71-1-149-151/}
}
TY  - JOUR
AU  - Tomasz Łuczak
AU  - Tomasz Schoen
TI  - On strongly sum-free subsets of abelian groups
JO  - Colloquium Mathematicum
PY  - 1996
SP  - 149
EP  - 151
VL  - 71
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-71-1-149-151/
DO  - 10.4064/cm-71-1-149-151
LA  - en
ID  - 10_4064_cm_71_1_149_151
ER  - 
%0 Journal Article
%A Tomasz Łuczak
%A Tomasz Schoen
%T On strongly sum-free subsets of abelian groups
%J Colloquium Mathematicum
%D 1996
%P 149-151
%V 71
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-71-1-149-151/
%R 10.4064/cm-71-1-149-151
%G en
%F 10_4064_cm_71_1_149_151
Tomasz Łuczak; Tomasz Schoen. On strongly sum-free subsets of abelian groups. Colloquium Mathematicum, Tome 71 (1996) no. 1, pp. 149-151. doi : 10.4064/cm-71-1-149-151. http://geodesic.mathdoc.fr/articles/10.4064/cm-71-1-149-151/

Cité par Sources :