On the exponent of the Weak commutativity group $\chi (G)$

R. Bastos, E. de Melo, R. de Oliveira

The weak commutativity group $\chi (G)$ is generated by two isomorphic groups $G$ and $G^{\phi }$ subject to the relations $[g,g^{\phi }]=1$ for all $g\in G$. The group $\chi (G)$ is an extension o…