Definition:Fixed Element of Permutation/Set of Fixed Elements

Definition
Let $S$ be a set.

Let $\pi: S \to S$ be a permutation on $S$.

The set of elements of $S$ which are fixed by $\pi$ can be denoted $\Fix \pi$.

Note that:
 * $x \notin S \implies x \in \Fix \pi$

Also see

 * Definition:Support of Permutation