On convex subgroups of right-ordered groups (Q1920831)

We call a subgroup \(H\) of a right-orderable group \(G\) a \(b\)-subgroup if it is convex in some linear right order on \(G\). In the present article, we prove that divisible central subgroups and normal divisible nilpotent subgroups of finite rank in a right-orderable group are \(b\)-subgroups. We show that the commutant of a solvable right-orderable group extending an abelian group by a finitely generated group is included in a proper \(b\)-subgroup.