Abstract
Let G, H be groups that act compatibly on each other and consider the non-abelian tensor product \(G \otimes H\). We prove that the set of all tensors \(T_{\otimes }(G,H)=\{g\otimes h{:}\,g \in G,\,h\in H\}\) is finite if and only if the non-abelian tensor product \(G \otimes H\) is finite. Further, we examine a finiteness criterion for \(G \otimes H\), when G and H are FC-groups. We also establish a sufficient condition for a finitely generated non-abelian tensor product to be finite. Some finiteness conditions for G in terms of certain torsion elements of the non-abelian tensor square \(G \otimes G\) are also studied.
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Communicated by A. Constantin.
This work was partially supported by FAPDF - Brazil, Grant: 0193.001344/2016.
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Bastos, R., Nakaoka, I.N. & Rocco, N.R. Finiteness conditions for the non-abelian tensor product of groups. Monatsh Math 187, 603–615 (2018). https://doi.org/10.1007/s00605-017-1143-x
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DOI: https://doi.org/10.1007/s00605-017-1143-x