# Coprime automorphism-faithful subgroup

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.