# Category:Automorphism Groups

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This category contains results about **Automorphism Groups**.

Definitions specific to this category can be found in Definitions/Automorphism Groups.

Let $\struct {S, *}$ be an algebraic structure.

Let $\mathbb S$ be the set of automorphisms of $S$.

Then the algebraic structure $\struct {\mathbb S, \circ}$, where $\circ$ denotes composition of mappings, is called the **automorphism group** of $S$.

The structure $\struct {S, *}$ is usually a group. However, this is not necessary for this definition to be valid.

The **automorphism group of $S$** is denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ as $\Aut S$.

## Subcategories

This category has only the following subcategory.

### E

## Pages in category "Automorphism Groups"

The following 8 pages are in this category, out of 8 total.