ON COMPUTING THE NON-ABELIAN TENSOR SQUARES OF THE FREE 2-ENGEL GROUPS

Abstract

AbstractIn 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.AMS 2000 Mathematics subject classification: Primary 20F05; 20F45. Secondary 20F18