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