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

Abstract

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

Cited by in corpus (2)

• The non-abelian tensor square of residually finite groups
• A note on finiteness conditions for the non-abelian tensor square of groups