Finiteness conditions for the box-tensor product of groups and related constructions

Abstract

We study finiteness conditions and closure properties for the box-tensor product G⊠H and related constructions. The content of this paper extends some results concerning the non-abelian tensor product of groups G⊗H. In particular, we deduce a quantitative version of the finiteness criterion for the non-abelian tensor product. Moreover, we obtain finiteness conditions for some functors that arise out of the non-abelian tensor square of groups, such as the second homology group H2(G), the non-abelian exterior square G∧G and the second stable homotopy group of an Eilenberg-MacLane space π2S(K(G,1)).