# 20.2 Operations for Permutations

`p1 * p2`

The operator `*` evaluates to the product of the two permutations p1 and p2.

`p1 / p2`

The operator `/` evaluates to the quotient p1 * p2^{-1} of the two permutations p1 and p2.

`LeftQuotient( p1, p2 )`

`LeftQuotient` returns the left quotient p1^{-1} * p2 of the two permutations p1 and p2. (This can also be written `p1 mod p2`.)

`p ^ i`

The operator `^` evaluates to the i-th power of the permutation p.

`p1 ^ p2`

The operator `^` evaluates to the conjugate p2^{-1} * p1 * p2 of the permutation p1 by the permutation p2.

`Comm( p1, p2 )`

`Comm` returns the commutator p1^{-1} * p2^{-1} * p1 * p2 of the two permutations p1 and p2.

`i ^ p`

The operator `^` evaluates to the image i^p of the positive integer i under the permutation p.

`i / p`

The operator `/` evaluates to the preimage i^{p^{-1}} of the integer i under the permutation p.

`list * p`
`p * list`

The operator `*` evaluates to the list of products of the permutations in list with the permutation p. That means that the value is a new list new such that `new[i] = list[i] * p` respectively `new[i] = p * list[i]`.

`list / p`

The operator `/` evaluates to the list of quotients of the permutations in list with the permutation p. That means that the value is a new list new such that `new[i] = list[i] / p`.

For the precedence of the operators see Operations.

GAP 3.4.4
April 1997