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- W2304579103 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." @default.
- W2304579103 created "2016-06-24" @default.
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- W2304579103 date "2016-03-22" @default.
- W2304579103 modified "2023-09-27" @default.
- W2304579103 title "A note on finiteness conditions for the non-abelian tensor square of groups" @default.
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