Definition:Characteristic Subgroup

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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.