On residually finite groups satisfying an Engel type identity.

Abstract

Let n, q be positive integers. We show that if G is a finitely generated residually finite group satisfying the identity [x,n yq ] ≡ 1, then there exists a function f (n) such that G has a nilpotent subgroup of finite index of class at most f (n). We also extend this result to locally graded groups.