Suppose we have a given permutation group that acts on a set of n elements.

If we pick k elements of the set, the stabilizer subgroup of those k elements is a subgroup of the given permutation group that keeps those elements unchanged.

Note that an analogous definition can be given for non-finite groups. Also note that the case for all finite groups is covered by the permutation definition since all groups are isomorphic to a subgroup of the symmetric group

TODO existence and uniqueness. Existence is obvious for the identity permutation, but proper subgroup likely does not exist in general.

- Permutation group | 0, 224, 6
- Permutation | 0, 304, 11
- Important discrete mathematical group | 0, 425, 18
- Important mathematical group | 0, 425, 19
- Group | 0, 5k, 89
- Algebra | 0, 8k, 171
- Mathematics | 17, 28k, 633
- Ciro Santilli's Homepage | 262, 218k, 4k

- Mathieu group | 239, 427, 13