# Coprime automorphism-invariant subgroup

From Groupprops

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

Suppose is a finite group and is a subgroup of . We say that is a **coprime automorphism-invariant subgroup** of if, for any automorphism of whose order is relatively prime to the order of , we have .