Finiteness Conditions for the $n$-fold Tensor Product of Groups

R. Bastos; G. Ortega

doi:10.1142/S0219498825502287

Finiteness Conditions for the $n$-fold Tensor Product of Groups

Group Theory 2025-10-28 v1

Authors: R. Bastos , G. Ortega

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Abstract

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 $\gamma_n(G)$ is finitely presented. We also examine some finiteness conditions for the non-abelian tensor product of groups.

Keywords

finitely generated group tensor product of groups polycyclic group finitely presented group non-abelian tensor product lower central series

Cite

@article{arxiv.2303.09633,
  title  = {Finiteness Conditions for the $n$-fold Tensor Product of Groups},
  author = {R. Bastos and G. Ortega},
  journal= {arXiv preprint arXiv:2303.09633},
  year   = {2025}
}

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