The non-abelian tensor product $G \otimes H$ of groups G and H was
introduced by Brown and Loday, following works of Miller and
Dennis. Ellis showed the finiteness of the
non-abelian tensor product $G \otimes H$ when both $G$ and $H$ are finite. 

I will present some related results concerning the (local) finiteness of the non-abelian tensor product $G \otimes H$.

This is a joint work with Nora\'i Rocco (Universidade de Bras\'ilia) e Irene Nakaoka (Universidade Estadual de Maring\'a).