On computing the non-abelian tensor squares of the free 2-engel groups

Abstract

In this paper we compute the non-abelian tensor square for the free 2-Engel group of rank n > 3. The non-abelian tensor square for this group is a direct product of a free abelian group and a nilpotent group of class 2 whose derived subgroup has exponent 3. We also compute the non-abelian tensor square for one of the group's finite homomorphic images, namely, the Burnside group of rank n and exponent 3.