Linearity problem for non-abelian tensor products

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In this paper we give an example of a linear group such that its tensor square is not linear. Also, we formulate some sufficient conditions for the linearity of non-abelian tensor products G circle times H and tensor squares G circle times G. Using these results we prove that tensor squares of some groups with one relation and some knot groups are linear. We prove that the Peiffer square of a finitely generated linear group is linear. At the end we construct faithful linear representations for the non-abelian tensor square of a free group and free nilpotent group.

Original languageEnglish
Pages (from-to)269-281
Number of pages13
JournalHomology, Homotopy and Applications
Issue number1
Publication statusPublished - 1 Jan 2019


  • Faithful linear representation
  • Linear group
  • Non-abelian tensor product
  • non-abelian tensor product
  • linear group
  • faithful linear representation


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