\begin{definition}[Definition:Operation Induced by Permutation]
Let $\struct {S, \circ}$ be an algebraic structure on a set $S$.
Let $\sigma: S \to S$ be a permutation on $S$.
Let $\circ_\sigma$ be the operation on $S$ defined as:
:$\forall x, y \in S: x \circ_\sigma y := \map \sigma {x \circ y}$
Then $\circ_\sigma$ is the '''operation (on $S$) induced by $\sigma$'''.
\end{definition}