# 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

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## Definition

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

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