Geodesic
A Class of Right-Orderable Groups
Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 648-654

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

A group g is called right-orderable (or an ro-group) if there exists an order relation ≦ on g such that a ≦ b implies ac ≦ be for all a, b, c in g. this is equivalent to the existence of a subsemigroup p of g such that p ⋂ p-1 = {e} and p ⋃ p-1 = g. given the order relation ≦, p can be taken to be the set of positive elements and conversely, given p, define a ≦ b if and only if ba-1 ε p. a group g together with a given right-order relation on g is called right-ordered. 
Mura, R. T. Botto; Rhemtulla, A. H. A Class of Right-Orderable Groups. Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 648-654. doi: 10.4153/CJM-1977-066-x
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