\begin{definition}[Definition:Closed under Inversion]
Let $\struct {G, \circ}$ be an group with an identity element $e$.
Let $H \subseteq G$ be a subset of $G$.
Then $H$ is '''closed under inversion''' {{iff}}:
:$\forall h \in H: h^{-1} \in H$
That is, {{iff}} the inverse of every element of $H$ is itself in $H$.
\end{definition}