Monatshefte für Mathematik

, Volume 187, Issue 4, pp 603–615 | Cite as

Finiteness conditions for the non-abelian tensor product of groups

  • R.  Bastos
  • I. N. Nakaoka
  • N. R.  Rocco


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.


Local properties Locally finite groups Non-abelian tensor product of groups 

Mathematics Subject Classification

20E25 20F50 20J06 


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© Springer-Verlag GmbH Austria, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade de BrasíliaBrasíliaBrazil
  2. 2.Departamento de MatemáticaUniversidade Estadual de MaringáMaringáBrazil

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