Linear Groups with Almost Right Engel Elements

Abstract

AbstractLet G be a linear group such that for every g ∈ G there is a finite set ${\cal R}(g)$ with the property that for every x ∈ G all sufficiently long commutators [g, x, x, …, x] belong to ${\cal R}(g)$. We prove that G is finite-by-hypercentral.