Definition:Permutation Group

Definition
A permutation group on a set $S$ is a subgroup of the group of permutations $\left({\Gamma \left({S}\right), \circ}\right)$ on $S$.

Also known as
Some sources call this a group of permutations, but this can easily be confused with the group of permutations.

A permutation group is sometimes referred to as a concrete group, based on the idea that it is a specific instantiation of a group which can be perceived as such in its own right, as opposed to an abstract group which consists purely of a set with an abstractly defined operation.