2-Engel relations between subgroups

In this paper we study groups G generated by two subgroups A and B   such that 〈a,b〉〈a,b〉 is nilpotent of class at most 2 for all a∈Aa∈A and b∈Bb∈B. A detailed description of the structure of such groups is obtained, generalizing the classical result of Hopkins and Levi on 2-Engel groups.