Geodesic
On a Theorem on Ordered Groups
Glasgow mathematical journal, Tome 4 (1958) no. 1, pp. 16-21

Voir la notice de l'article provenant de la source Cambridge University Press

The following work establishes a new proof of the theorem: Every archimedean ordered group is abelian. This theorem has been proved differently by many authors. It was first proved by O. Hölder [2]. A second proof has been given by H. Cartan [1]: he uses the topology which is naturally introduced in the group by its order. 
Chehata, C. G. On a Theorem on Ordered Groups. Glasgow mathematical journal, Tome 4 (1958) no. 1, pp. 16-21. doi: 10.1017/S2040618500033785
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[1] 1.Cartan, H., Un théorème sur les groupes ordonnès, Bull. Sci. Math., 63 (1939), 201–205. Google Scholar

[2] 2.Hölder, O., Die Axiome der Quantitat and die Lehre von Mass, Ber. Verh. Säclis. Ges. Wisa. Leipzig Math.-Phys. Cl., 53 (1901), 1–64. Google Scholar

[3] 3.Levi, F. W., Ordered groups, Proc. Indian Acad. Sci., 16 (1942), 256–263. Google Scholar | DOI

[4] 4.Levi, F. W., Contributions to the theory of ordered groups, Proc. Indian Acad. Sci., 17 (1943), 199–201. Google Scholar | DOI

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