Geodesic
Order-automorphism groups of Archimedean ordered groups
Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 628-633

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DOI

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.
DOI : 10.4153/S0008439524000973
Mots-clés : Ordered group, Archimedean, order-preserving automorphism 
Marks, Greg. Order-automorphism groups of Archimedean ordered groups. Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 628-633. doi: 10.4153/S0008439524000973
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     title = {Order-automorphism groups of {Archimedean} ordered groups},
     journal = {Canadian mathematical bulletin},
     pages = {628--633},
     year = {2025},
     volume = {68},
     number = {2},
     doi = {10.4153/S0008439524000973},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000973/}
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