= Stabilizer
{disambiguate=group}
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.
Bibliography:
* https://mathworld.wolfram.com/Stabilizer.html
* https://ncatlab.org/nlab/show/stabilizer+group from <NLab>