Geodesic
Some conditions of Infinite Subsets of Infinite Groups
Bulletin of the Malaysian Mathematical Society, Tome 22 (1999) no. 1 
Alireza Abdollahi; Bijan Taeri. Some conditions of Infinite Subsets of Infinite Groups. Bulletin of the Malaysian Mathematical Society, Tome 22 (1999) no. 1. http://geodesic.mathdoc.fr/item/BMMS_1999_22_1_a8/
@article{BMMS_1999_22_1_a8,
     author = {Alireza Abdollahi and Bijan Taeri},
     title = {Some conditions of {Infinite} {Subsets} of {Infinite} {Groups}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {1999},
     volume = {22},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_1999_22_1_a8/}
}
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Voir la notice de l'article provenant de la source BMMS

Let G be an infinite group. In this note we prove the following: For all if and only if every two infinite subsets X and Y of G contain elements x and y , respectively such that Also if then for all if and only if every two infinite subsets X and Y of G contain elements x and y , respectively such that