2016/11/22 by Raimundo Bastos, R. Bastos, Irene N. Nakaoka +3
Mathematics · #Advanced Operator Algebra Research #Cartesian tensor #Finite Group Theory Research #Limits and Structures in Graph Theory #Tensor (intrinsic definition) #Tensor contraction #Tensor density #Tensor product #Tensor product of Hilbert spaces #Tensor product of algebras #Tensor product of modules #math.GR #msc:20E25 #msc:20F50 #msc:20J06
paper · pdf · doi:10.1007/s00605-017-1143-x
published as Monatshefte fur Mathematik, December 2018, Volume 187, Issue 4, pp 603--615 · The content of this paper improves and extends the main results of arXiv:1603.07003 [math.GR]
arxiv created 2016/11/22 · openalex created_date 2016/11/30 · openalex publication_date 2017/12/09 · arxiv updated 2018/10/23 · openalex updated_date 2026/08/05
Let G, H be groups. We denote by η(G,H) a certain extension of the non-abelian tensor product G ⊗ H by G × H. We prove that if G and H are groups that act compatibly on each other and such that the set of all tensors T⊗(G,H)=\g⊗ h : g ∈ G, h∈ H\ is finite, then the non-abelian tensor product G ⊗ H is finite. In the opposite direction we examine certain finiteness conditions of G in terms of similar conditions for the tensor square G ⊗ G.