Right 2-Engel element

Definition
Suppose $$G$$ is a group and $$x$$ is an element of $$G$$. We say that $$x$$ is a right 2-Engel element if it satisfies the following equivalent conditions:


 * $$[y,[y,x]]$$ is the identity element for all $$y \in G$$.
 * $$[[x,y],y]$$ is the identity element for all $$y \in G$$.