Definition:Structure 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 $S$ induced by $\sigma$:
 * $\forall x, y \in S: x \circ_\sigma y := \map \sigma {x \circ y}$

Then $\struct {S, \circ_\sigma}$ is the (algebraic) structure induced by $\sigma$ (on $\circ$).