Convex subgroup of an ordered group
= Convex subgroup of an ordered group
A <subgroup> $C$ is convex if $c_1\le g\le c_2$ with $c_1,c_2\in C$ implies $g\in C$. In a <linearly ordered group>, convex subgroups form a chain under inclusion: positive elements witnessing incomparability would be comparable and force the smaller one into the other subgroup by convexity.