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

Raimundo Bastos; Norai R. Rocco

doi:10.1007/s00013-016-0930-2

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

Group Theory 2016-09-06 v1

Authors: Raimundo Bastos , Norai R. Rocco

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Abstract

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 $\nu(G)$ (Theorem B).

Keywords

non-abelian tensor square finite-by-nilpotent groups nilpotent-by-finite BFC-groups group extension

Cite

@article{arxiv.1509.05114,
  title  = {Non-abelian tensor square of finite-by-nilpotent groups},
  author = {Raimundo Bastos and Norai R. Rocco},
  journal= {arXiv preprint arXiv:1509.05114},
  year   = {2016}
}

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