Trivial Subgroup and Group Itself are Normal

Theorem

Trivial Subgroup is Normal

Let $\struct {G, \circ}$ be a group whose identity is $e$.

Then the trivial subgroup $\struct {\set e, \circ}$ of $G$ is a normal subgroup in $G$.


Group is Normal in Itself

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

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

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