# On $n$-Kappe groups

Document Type: Research Paper

Authors

1 Damghan University

2 Gonbad-e Qabus University

Abstract

Let $G$ be an infinite group and $n\in \{3‎, ‎6\}\cup\{2^k| k\in \mathbb{N}\}$‎. ‎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 $[x^n‎, ‎y‎, ‎y]=1$‎.

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