Group-theoretic commutator, defined as *[x,y]=x^(-1)y^(-1)xy*

1 | ```
commutator(x, y)
``` |

`x,y` |
Permutation objects, coerced to word |

Robin K. S. Hankin

`group_action`

1 2 3 4 5 6 7 8 9 10 | ```
x <- rperm(10,7)
y <- rperm(10,8)
z <- rperm(10,9)
uu <-
commutator(commutator(x,y),z^x) *
commutator(commutator(z,x),y^z) *
commutator(commutator(y,z),x^y)
stopifnot(all(is.id(uu))) # this is the Hall-Witt identity
``` |

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