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 $H$.
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Subgroups