# Category:Inner Automorphisms

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This category contains results about **Inner Automorphisms**.

Let $G$ be a group.

Let $x \in G$.

Let the mapping $\kappa_x: G \to G$ be defined such that:

- $\forall g \in G: \map {\kappa_x} g = x g x^{-1}$

$\kappa_x$ is called the **inner automorphism of $G$ (given) by $x$**.

## Subcategories

This category has only the following subcategory.

## Pages in category "Inner Automorphisms"

The following 11 pages are in this category, out of 11 total.

### I

- Image of Mapping from Group Element to Inner Automorphism is Inner Automorphism Group
- Inner Automorphism Group is Isomorphic to Quotient Group with Center
- Inner Automorphism is Automorphism
- Inner Automorphism Maps Subgroup to Itself iff Normal
- Inner Automorphisms form Normal Subgroup of Automorphism Group
- Inner Automorphisms form Subgroup of Automorphism Group
- Inner Automorphisms form Subgroup of Symmetric Group
- Inverse of Inner Automorphism