ORDERED GROUPS IN WHICH ALL CONVEX JUMPS ARE CENTRAL Bludov, V.V.; Glass, A.M.W.; Rhemtulla, Akbar H.;
(G, <) is an ordered group if'<'is a total order relation on G in which f < g implies that xfy < xgy for all f, g, x, y G. We say that (G, <) is centrally ordered if (G, <) is ordered and ［G,D］ C for every convex jump C D in G. Equivalently, if for all f, g G with g > 1. Every order on a torsion-free locally nilpotent group is central. We prove that if every order on every two-generator subgroup of a locally soluble orderable group G is central, then G is locally nilpotent. We also provide an example of a non-nilpotent two-generator metabelian orderable group in which all orders are central.