Engel-type subgroups and length parameters of finite groups

Evgeny Khukhro, Pavel Shumyatsky

Let $g$ be an element of a finite group $G$. For a positive integer $n$, let $E_n(g)$ be the subgroup generated by all commutators $[...[[x,g],g],\dots ,g]$ over $x\in G$, where $g$…