Noraí Rocco

On some series of a group related to the non-abelian tensor square of groups

Let $G$ be a group. We denote by $ν(G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$. In this paper we prove that the derived subgroup $ν(G)'$ is a central product of three normal subgroups of $ν(G)$, all isomorphic to the non-abelian tensor square $G \otimes G$. As a consequence, we describe the structure of each term of the derived and lower central series of the group $ν(G)$.