Bounded Engel group

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Definition

A group $G$ is termed a $n$-Engel group if, for any $x,y\in G$, there exists $n$ such that:

$[[\dots [x,y],y],\dots ,y]=e$

where the $y$ occurs $n$ times.

A group that is $n$-Engel for some positive integer $n$, is termed a bounded Engel group.

Relation with other properties

Weaker properties

• Engel group
• Nilpotent group: In fact a group of nilpotency class $c$ is a $c$-Engel group.