Fixed-point subgroup

In algebra, the fixed-point subgroup $G^{f}$ of an automorphism f of a group is the subgroup of G:

$G^{f}=\{g\in G|f(g)=g\}$.

For example, take G to be the group of invertible n-by-n real matrices and $f(g)=(g^{-1})^{T}$. Then $G^{f}$ is the group $O(n)$ of n-by-n orthogonal matrices.