Finiteness conditions for the non-abelian tensor product of groups
| Autor: | Bastos, Raimundo, Nakaoka, Irene N., Rocco, Noraí R. |
|---|---|
| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Monatshefte fur Mathematik, December 2018, Volume 187, Issue 4, pp 603--615 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00605-017-1143-x |
| Popis: | 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 $G \otimes G$. Comment: The content of this paper improves and extends the main results of arXiv:1603.07003 [math.GR] |
| Databáze: | arXiv |
| Externí odkaz: |
|