Permutation group

A permutation is a way to rearrange the elements of a set. The set of all possible permutations of $n$ objects forms a group, called the symmetric group $S_n$. The group operation is 'doing one rearrangement after another.'

Important properties

• The identity permutation leaves every element in its place.

• Every permutation has an inverse that undoes its rearrangement.

• The group operation (composition) is associative.

• The number of permutations of $n$ objects is $n!$.