# Category:Inversion Mappings

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This category contains results about **Inversion Mappings**.

Definitions specific to this category can be found in Definitions/Inversion Mappings.

Let $\struct {G, \circ}$ be a group.

The **inversion mapping** on $G$ is the mapping $\iota: G \to G$ defined by:

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

That is, $\iota$ assigns to an element of $G$ its inverse.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Inversion Mappings"

The following 10 pages are in this category, out of 10 total.

### I

- Inversion Mapping is Automorphism iff Group is Abelian
- Inversion Mapping is Involution
- Inversion Mapping is Isomorphism from Ordered Abelian Group to its Dual
- Inversion Mapping is Isomorphism to Opposite Group
- Inversion Mapping is Mapping
- Inversion Mapping is Permutation
- Inversion Mapping on Ordered Group is Dual Order-Isomorphism
- Inversion Mapping on Topological Group is Homeomorphism
- Inversion Mapping Reverses Ordering in Ordered Group