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

Let $G$ be a group. We denote by $ν(G)$ 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, $ν(G)$ is nilpotent-by-finite (Theorem A). Also we characterize BFC-groups in terms of $ν(G)$ (Theorem B).

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