Definition:Characteristic Subset
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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 $G$.
Also see
Sources
- 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation