Definition:Characteristic Subgroup
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Definition
Let $G$ be a group.
Let $H$ be a subgroup such that:
- $\forall \phi \in \Aut G: \phi \sqbrk H = H$
where $\Aut G$ is the automorphism group of $G$.
Then $H$ is characteristic (in $G$), or a characteristic subgroup of $G$.
Also see
- Results about characteristic subgroups can be found here.
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Group Homomorphism and Isomorphism: $\S 64 \epsilon$