# 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