L^{-1}$ and $\beta=U$. A sequence of the form $\alpha \beta \alpha^{-1} \beta^{-1}$ is called a commutator and is very useful when studying permuations. The following square bracket notation is used ...

In a dynamo, a split ring commutator changes the coil connections every half turn. As the induced potential difference is about to change direction, the connections are reversed. This means that ...