Geodesic
A Combinatorial Problem in Infinite Group
Bulletin of the Malaysian Mathematical Society, Tome 25 (2002) no. 2 
Alireza Abdollahi. A Combinatorial Problem in Infinite
                        Group. Bulletin of the Malaysian Mathematical Society, Tome 25 (2002) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2002_25_2_a1/
@article{BMMS_2002_25_2_a1,
     author = {Alireza Abdollahi},
     title = {A {Combinatorial} {Problem} in {Infinite
}                        {Group}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2002},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2002_25_2_a1/}
}
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Voir la notice de l'article provenant de la source BMMS

Let be a word in the free group of rank and let be the variety of groups defined by the law . Define to be the class of all groups in which for any infinite subsets there exist , , such that . Clearly, ; being the class of finite groups. In this paper, we investigate some words w and some certain classes of groups for which the equality holds.