Definition:Characteristic Subset

Definition
Let $G$ be a group.

Let $S \subseteq G$ be a subset of $G$ such that:
 * $\forall \phi \in \operatorname{Aut} \left({G}\right): \phi \left({S}\right) = S$

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

Then $S$ is characteristic (in $G$), or a characteristic subset of $G$.

Also see

 * Definition:Characteristic Subgroup