Non-abelian tensor square of finite-by-nilpotent groups

Abstract

Let G be a group. We denote by ν(G) an extension of the non-abelian tensor square G ⊗ G by G × G. We prove that if G is finite-by-nilpotent, then the non-abelian tensor square G ⊗ G is finite-by-nilpotent. Moreover, ν(G) is nilpotent-by-finite (Theorem A). Also we characterize BFC-groups in terms of ν(G) (Theorem B).

On some closure properties of the non-abelian tensor product

“…We also prove that if G and H are supersolvable groups, then G ⊗ H is a supersolvable group. Recently the authors of [2] prove that the non-abelian tensor square of nilpotent by finite group is a nilpotent by finite group. We prove that the non-abelian tensor product of nilpotent by finite groups is a nilpotent by finite group.…”