Trivial Subgroup and Group Itself are Normal
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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.