# Category:Characteristic Subgroups

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This category contains results about **Characteristic Subgroups**.

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 $G$**.

## Pages in category "Characteristic Subgroups"

The following 3 pages are in this category, out of 3 total.