Finite groups with Engel sinks of bounded rank

E. I. Khukhro, P. Shumyatsky

For an element $g$ of a group $G$, an Engel sink is a subset $\mathcal{E}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[x,g],g],\dots ,g]$ belong to ${…