# Category:Ordered Groups

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

An **ordered group** is an ordered structure $\struct {G, \circ, \preceq}$ such that $\struct {G, \circ}$ is a group..

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Ordered Groups"

The following 24 pages are in this category, out of 24 total.

### D

- User:Dfeuer/Archimedean Totally Ordered Group is Abelian
- User:Dfeuer/Archimedean Totally Ordered Group is Abelian/Lemma 1
- User:Dfeuer/Archimedean Totally Ordered Group is Abelian/Lemma 2
- User:Dfeuer/Complete Totally Ordered Group is Archimedean
- User:Dfeuer/Totally Ordered Group with Order Topology is Topological Group

### I

- Infima in Ordered Group
- Infimum of Subset Product in Ordered Group
- Inverse of Infimum in Ordered Group is Supremum of Inverses
- Inverse of Supremum in Ordered Group is Infimum of Inverses
- Inversion Mapping is Isomorphism from Ordered Abelian Group to its Dual
- Inversion Mapping on Ordered Group is Dual Order-Isomorphism
- Inversion Mapping Reverses Ordering in Ordered Group