\begin{definition}[Definition:Characteristic Subset]
Let $G$ be a group.
Let $S \subseteq G$ be a subset of $G$ such that:
:$\forall \phi \in \Aut G: \map \phi S = S$
where $\Aut G$ is the automorphism group of $G$.
Then $S$ is  '''characteristic (in $G$)''', or '''a characteristic subset of $G$'''.
\end{definition}