Right-relative convexity of subgroups of right-orderable groups (Q1916587)

By a Conrad right-orderable group the author understands a group that possesses a system of subgroups that is complete relative to unions and intersections, is subnormal and linearly ordered by inclusion. The following theorems are proved: Theorem 1. Let \(G\) be a Conrad right-orderable group and let \(H\) be a normal subgroup of \(G\) which is isomorphic to the additive group \(\mathbb{Q}\) of the rational numbers. Then \(H\) is right-relative convex. Theorem 2. A complete subgroup \(H\) of the center of a Conrad right-orderable group \(G\) is right-relative convex.