On the probability of being a 2-Engel group

On the probability of being a 2-Engel group

‎Let $G$ be a finite group and $d_2(G)$ denotes the probability‎that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $G$‎. ‎We‎will obtain lower and upper bounds for $d_2(G)$ in the case where‎the sets $E_G(x)={yin G:[y,x,x]=1}$ are subgroups of $G$ for‎all $xin G$‎. ‎Also the given examples illus...

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Bibliographic Details
Main Authors: Ahmad Erfanian, Mohammad Farrokhi Derakhshandeh Ghouchan
Format: Article
Language:English
Published: University of Isfahan 2013-12-01
Series:International Journal of Group Theory
Subjects:
Probability‎
‎2-Engel condition‎
3-metabelian
Online Access:http://www.theoryofgroups.ir/?_action=showPDF&article=2836&_ob=8c5fc82980e41cf440902a6770e2cb2e&fileName=full_text.pdf.
Description
Summary:‎Let $G$ be a finite group and $d_2(G)$ denotes the probability‎that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $G$‎. ‎We‎will obtain lower and upper bounds for $d_2(G)$ in the case where‎the sets $E_G(x)={yin G:[y,x,x]=1}$ are subgroups of $G$ for‎all $xin G$‎. ‎Also the given examples illustrate that all the‎bounds are sharp.
ISSN:2251-7650
2251-7669

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