Definition:Operation Induced by Permutation

Definition
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 $\sigma$.