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

Abstract

Let $G$ be a group. We denote by $\nu (G)$ 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 $\nu (G{)}^{\prime }$ is a central product of three normal subgroups of $\nu (G)$, 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 $\nu (G)$.

References in corpus (1)

• Non-abelian tensor square and related constructions of $p$-groups

Cited by in corpus (1)

• Finiteness Conditions for the $n$-fold Tensor Product of Groups