Trivial subgroup is characteristic
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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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.