# Definition:Characteristic Subset

## Definition

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 $G$.