Groups generated by a finite Engel set

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 . 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.