Geodesic
Embedding rank one simple groups into rank one simple Riesz groups
Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 551-567

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DOI

We give a method for embedding a large family of partially ordered simple groups of rank one into simple Riesz groups of rank one. In particular, we answer in the affirmative a question of Wehrung, by constructing a torsion-free, simple Riesz group G of rank one containing an interval D\varsubsetneqq G^+ such that 2D=G^+. We sketch some potential applications of this result in the context of monoids of intervals and K-Theory of rings. 
Pardo, E. Embedding rank one simple groups into rank one simple Riesz groups. Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 551-567. doi: 10.1017/S0017089502030185
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     title = {Embedding rank one simple groups into rank one simple {Riesz} groups},
     journal = {Glasgow mathematical journal},
     pages = {551--567},
     year = {2002},
     volume = {44},
     number = {3},
     doi = {10.1017/S0017089502030185},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502030185/}
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