Inclusion Mapping on Subgroup is Monomorphism
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Theorem
Let $\struct {G, \circ}$ be a group.
Let $\struct {H, \circ {\restriction_H} }$ be a subgroup of $G$.
Let $i: H \to G$ be the inclusion mapping from $H$ to $G$.
Then $i$ is a group monomorphism.
Proof
We have:
The result follows by definition of (group) monomorphism.
$\blacksquare$
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Quotient Groups