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, if G acts on a set X and x an element of X and if $f(g)=g\cdot x$, then $G^{f}$ is the stabilizer of x.