arXiv subjects
Publications and source records attributed to Ricardo de Oliveira.
The weak commutativity group $χ(G)$ is generated by two isomorphic groups $G$ and $G^{φ}$ subject to the relations $[g,g^φ]=1$ for all $g \in G$. We obtain new expressions for the terms of the derived series and the lower central series of $χ(G)$. We also present new bounds for the exponent of some sections of $χ(G)$.
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 $ν(G)$.