Finiteness conditions for the non-abelian tensor product of groups

Abstract

Let $G$, $H$ be groups. We denote by $\eta (G,H)$ a certain extension of the non-abelian tensor product $G\otimes H$ by $G\times H$. We prove that if $G$ and $H$ are groups that act compatibly on each other and such that the set of all tensors $T_{\otimes }(G,H)=\{g\otimes h:g\in G,h\in H\}$ is finite, then the non-abelian tensor product $G\otimes H$ is finite. In the opposite direction we examine certain finiteness conditions of $G$ in terms of similar conditions for the tensor square $G\otimes G$.

The content of this paper improves and extends the main results of arXiv:1603.07003 [math.GR]

References in corpus (1)

• The non-abelian tensor square of residually finite groups

Cited by in corpus (2)

• Finiteness of homotopy groups related to the non-abelian tensor product
• Finiteness Conditions for the $n$-fold Tensor Product of Groups