Definition:Closed under Inversion

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Definition

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 if and only if:

$\forall h \in H: h^{-1} \in H$


That is, if and only if the inverse of every element of $H$ is itself in $H$.


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