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On the probability of being a 2-Engel group | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 2، شماره 4، اسفند 2013، صفحه 31-38 اصل مقاله (411.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2836 | ||
| نویسندگان | ||
| Ahmad Erfanian؛ Mohammad Farrokhi Derakhshandeh Ghouchan* | ||
| Ferdowsi University of Mashhad | ||
| چکیده | ||
| Let $G$ be a finite group and $d_2(G)$ denotes the probability that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $G$. We will obtain lower and upper bounds for $d_2(G)$ in the case where the sets $E_G(x)=\{y\in G:[y,x,x]=1\}$ are subgroups of $G$ for all $x\in G$. Also the given examples illustrate that all the bounds are sharp. | ||
| کلیدواژهها | ||
| Probability؛ 2-Engel condition؛ 3-metabelian | ||
| مراجع | ||
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