Group is Normal in Itself

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Theorem

Let $\struct {G, \circ}$ be a group.

Then $\struct {G, \circ}$ is a normal subgroup of itself.


Proof

First we note that $\struct {G, \circ}$ is a subgroup of itself.


To show $\struct {G, \circ}$ is normal in $G$:

$\forall a, g \in G: a \circ g \circ a^{-1} \in G$

as $G$ is closed by definition.


Hence the result.

$\blacksquare$


Sources