\begin{definition}[Definition:Inversion Mapping]
Let $\struct {G, \circ}$ be a group.
The '''inversion mapping''' on $G$ is the mapping $\iota: G \to G$ defined by:
:$\forall g \in G: \map \iota g = g^{-1}$
That is, $\iota$ assigns to an element of $G$ its inverse.
\end{definition}