Coprime automorphism-faithful characteristic subgroup

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and coprime automorphism-faithful subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup $H$ of a finite group $G$ is termed copime automorphism-faithful characteristic if every automorphism of $G$ restricts to an automorphism of $H$ (i.e., $H$ is a characteristic subgroup) and if $K$ is the kernel of the map:

$\operatorname{Aut}(G) \to \operatorname{Aut}(H)$

defined by restriction, then every prime divisor of the order of $K$, divides the order of $G$.