Groups generated by a finite Engel set

Abstract

A subset S of a group G is called an Engel set if, for all x, y∈. S, there is a non-negative integer n=n(x, y) such that [x,ny]=1. In this paper we are interested in finding conditions for a group generated by a finite Engel set to be nilpotent. In particular, we focus our investigation on groups generated by an Engel set of size two. © 2011 Elsevier Inc.