Characteristic and self-centralizing implies coprime automorphism-faithful
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., self-centralizing characteristic subgroup) must also satisfy the second subgroup property (i.e., coprime automorphism-faithful subgroup)
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Any characteristic Self-centralizing subgroup (?) of a finite group is coprime automorphism-faithful: in particular, it is a Coprime automorphism-faithful characteristic subgroup (?).
Statement with symbols
This is a special case of a somewhat more general fact: