Geodesic
Right-Ordered Polycyclic Groups
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 175-178

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One of the features that make right-ordered groups harder to investigate than ordered groups is that their system of convex subgroups may fail to have the following property:(*) if C and C’ are convex subgroups of G and C’ covers C, then C is normal in C’ and C’/C is order-isomorphic to a subgroup of the naturally ordered additive group of real numbers. 
Mura, Roberta Botto. Right-Ordered Polycyclic Groups. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 175-178. doi: 10.4153/CMB-1974-035-9
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     author = {Mura, Roberta Botto},
     title = {Right-Ordered {Polycyclic} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {175--178},
     year = {1974},
     volume = {17},
     number = {2},
     doi = {10.4153/CMB-1974-035-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-035-9/}
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