Braid group relations (${\sigma }_i{\sigma }_{i+1}{\sigma }_i={\sigma }_{i+1}{\sigma }_i{\sigma }_{i+1}$)

The generators ${\sigma }_i$ commute when $|i-j|>1$ and satisfy ${\sigma }_i{\sigma }_{i+1}{\sigma }_i={\sigma }_{i+1}{\sigma }_i{\sigma }_{i+1}$. Unlike a symmetric-group presentation, there is no ${\sigma }_i^2=1$ relation.