1 results
Order-automorphism groups of Archimedean ordered groups
- Part of
-
- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 23 December 2024, pp. 1-6
-
- Article
-
- You have access
- HTML
- Export citation
-
The group of order-preserving automorphisms of a finitely generated Archimedean ordered group of rank
$2$ is either infinite cyclic or trivial according as the ratio in 
$\mathbb {R}$ of the generators of the subgroup is or is not quadratic over 
$\mathbb {Q}.$ In the case of an Archimedean ordered group of rank 
$2$ that is not finitely generated, the group of order-preserving automorphisms is free abelian. Criteria determining the rank of this free abelian group are established.
