A note on finiteness conditions for the non-abelian tensor square of groups

2016/03/22 by Bastos, Raimundo, Rocco, Noraí Romeu
#20E26 #20F50 #20J06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1603.07003

Abstract

Let G be a group. We denote by ν(G) a certain extension of the non-abelian tensor square G ⊗ G by G × G. We prove that if G is a finitely generated group in which the set of all simple tensors T_⊗(G) is finite, then the non-abelian tensor square G ⊗ G and the group ν(G) are finite. Moreover, we show that if G is a locally residually finite group in which the set of simple tensors T_⊗(H) is finite for every proper finitely generated subgroup H of G, then the group ν(G) is locally finite.

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