A note on finiteness conditions for the non-abelian tensor square of groups

Abstract

Let $G$ be a group. We denote by $\nu (G)$ a certain extension of the non-abelian tensor square $G\otimes G$ by $G\times G$. We prove that if $G$ is a finitely generated group in which the set of all simple tensors $T_{\otimes }(G)$ is finite, then the non-abelian tensor square $G\otimes G$ and the group $\nu (G)$ are finite. Moreover, we show that if $G$ is a locally residually finite group in which the set of simple tensors $T_{\otimes }(H)$ is finite for every proper finitely generated subgroup $H$ of $G$, then the group $\nu (G)$ is locally finite.

This paper has been withdrawn by the author due to important modifications to be done

References in corpus (1)

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