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 (i.e., a subset of the automorphism group 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 (called the Cartan involution). Then is the group of n-by-n orthogonal matrices. ; that is, the centralizer of S.
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