Structural Results On The Weak Commutativity Construction

Abstract

The weak commutativity group $\ddot{I}‡(G)$ is generated by two isomorphic groups $G$ and $G^{\ddot{I}†}$ subject to the relations $[g,g^{\ddot{I}}†]=1$ for all $g\in G$. We obtain new expressions for the terms of the derived series and the lower central series of $\ddot{I}‡(G)$. We also present new bounds for the exponent of some sections of $\ddot{I}‡(G)$.