Irrational ordered groups (Q1108299)

The authors deal with the ordered set \(I\) of irrational numbers which is groupable. In Theorem 4 they characterize those ordered groups carried by \(I\) in terms of their convex subgroups. They also make a number of observations about the possible group structure of ordered groups carried by \(I\). The resulting ordered group is severely restricted in its group structure and in the structure of its set of convex subgroups.