Trivial subgroup is characteristic

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This article gives the statement, and possibly proof, of a subgroup property (i.e., characteristic subgroup) satisfying a subgroup metaproperty (i.e., trivially true subgroup property)
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Statement

In any group, the trivial subgroup is a characteristic subgroup, i.e., any automorphism of the whole group maps the trivial subgroup to itself.

Proof

By definition, a homomorphism of groups must send the identity element to the identity element. Thus, any automorphism of a group must send its identity element to its identity element, and hence, must map the trivial subgroup to within itself.