# Coprime automorphism-faithful subgroup

From Groupprops

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Definition

A subgroup of a finite group is termed **coprime automorphism-faithful** if, given any non-identity automorphism such that , and such that the order of is relatively prime to the order of , acts nontrivially on . Equivalently, any coprime automorphism group of that acts trivially on must be trivial.