On n-Kappe groups

Let G be an infinite group and n\in \{۳‎, ‎۶\}\cup\{۲^k| k\in \mathbb{N}\}‎. ‎In this paper‎, ‎we prove that G is an n-Kappe group if and only if for any two infinite subsets X and Y of G‎, ‎there exist x\in X and y\in Y such that [x^n‎, ‎y‎, ‎y]=۱‎.

کلیدواژه ها:

‎Kappe groups‎ ، ‎Variety of groups‎ ، ‎Erd {o}s's Problem