Archiv der Mathematik

, Volume 107, Issue 2, pp 127–133 | Cite as

Non-abelian tensor square of finite-by-nilpotent groups

  • Raimundo Bastos
  • Noraí R. Rocco


Let G be a group. We denote by \({\nu(G)}\) an extension of the non-abelian tensor square \({G \otimes G}\) by \({G \times G}\). We prove that if G is finite-by-nilpotent, then the non-abelian tensor square \({G \otimes G}\) is finite-by-nilpotent. Moreover, \({\nu(G)}\) is nilpotent-by-finite (Theorem A). Also we characterize BFC-groups in terms of \({\nu(G)}\) among the groups G in which the derived subgroup is finitely generated (Theorem B).

Mathematics Subject Classification

Primary 20E34 20F24 Secondary 20F14 


Structure theorems Derived series FC-groups 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade de BrasíliaBrasiliaBrazil

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