Definition:Characteristic Subgroup

Definition
Let $G$ be a group.

Let $H$ be a subgroup such that:
 * $\forall \phi \in \operatorname{Aut} \left({G}\right): \phi \left({H}\right) = H$

where $\operatorname{Aut} \left({G}\right)$ is the group of automorphisms of $G$.

Then $H$ is characteristic (in $G$), or a characteristic subgroup of $G$.

Also see

 * Definition:Characteristic Subset