# Inclusion Mapping on Subgroup is Monomorphism

## 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.

$\blacksquare$