Definition:Characteristic Subgroup

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

• Definition:Characteristic Subset

• Results about characteristic subgroups can be found here.

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Group Homomorphism and Isomorphism: $\S 64 \epsilon$