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On $n$-Kappe groups | ||
| International Journal of Group Theory | ||
| مقاله 4، دوره 3، شماره 3، آذر 2014، صفحه 35-38 اصل مقاله (274.41 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2014.4434 | ||
| نویسندگان | ||
| Asadollah Faramarzi Salles* 1؛ Hassan Khosravi2 | ||
| 1Damghan University | ||
| 2Gonbad-e Qabus University | ||
| چکیده | ||
| 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 $[x^n, y, y]=1$. | ||
| کلیدواژهها | ||
| Kappe groups؛ Variety of groups؛ Erd"{o}s's Problem | ||
| مراجع | ||
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