# Coprime automorphism-faithful subgroup

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 $H$ of a finite group $G$ is termed coprime automorphism-faithful if, given any non-identity automorphism $\sigma \in \operatorname{Aut}(G)$ such that $\sigma(H) = H$, and such that the order of $\sigma$ is relatively prime to the order of $G$, $\sigma$ acts nontrivially on $H$. Equivalently, any coprime automorphism group of $G$ that acts trivially on $G$ must be trivial.