Fixed-point subgroup
In algebra, the fixed-point subgroup of an automorphism f of a group G is the subgroup of G:
More generally, if S is a set of automorphisms of G, then the set of the elements of G that are left fixed by every automorphism in S is a subgroup of G, denoted by GS.
For example, take G to be the group of invertible n-by-n real matrices and . Then is the group of n-by-n orthogonal matrices.
To give an abstract example, let S be a subset of a group G. Then each element s of S can be associated with the automorphism, i.e. conjugation by s. Then
that is, the centralizer of S.
