Finiteness Conditions for the $n$-fold Tensor Product of Groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914115506667520 |
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| author | Bastos, R. Ortega, G. |
| author_facet | Bastos, R. Ortega, G. |
| contents | Let $G$ be a finitely generated group. We prove that the $n$-fold tensor product $G^{\otimes n}$ is finite (resp. polycyclic) if and only $G$ is finite (resp. polycyclic). Further, assuming that $G$ is finitely presented, we show that $G^{\otimes n}$ is finitely presented if and only if $γ_n(G)$ is finitely presented. We also examine some finiteness conditions for the non-abelian tensor product of groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09633 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finiteness Conditions for the $n$-fold Tensor Product of Groups Bastos, R. Ortega, G. Group Theory 20E06, 20E22, 20E34, 20F18, 20F24, 20J99 Let $G$ be a finitely generated group. We prove that the $n$-fold tensor product $G^{\otimes n}$ is finite (resp. polycyclic) if and only $G$ is finite (resp. polycyclic). Further, assuming that $G$ is finitely presented, we show that $G^{\otimes n}$ is finitely presented if and only if $γ_n(G)$ is finitely presented. We also examine some finiteness conditions for the non-abelian tensor product of groups. |
| title | Finiteness Conditions for the $n$-fold Tensor Product of Groups |
| topic | Group Theory 20E06, 20E22, 20E34, 20F18, 20F24, 20J99 |
| url | https://arxiv.org/abs/2303.09633 |