Definition:Transplant (Abstract Algebra)

Theorem
Let $\struct {S, \circ}$ be an algebraic structure.

Let $f: S \to T$ be a bijection.

Let $\oplus$ be the one and only one operation such that $f: \struct {S, \circ} \to \struct {T, \oplus}$ is an isomorphism.

The operation $\oplus$ is called the transplant of $\circ$ under $f$.

Also see

 * Transplanting Theorem where it is shown that:
 * $\forall x, y \in T: x \oplus y = \map f {\map {f^{-1} } x \circ \map {f^{-1} } y}$