Solvable groups in which every maximal partial order is isolated
Roberta Botto Mura, A. H. Rhemtulla · Pacific Journal of Mathematics · 1974
It is shown that every maximal partial order in a torsionfree abelian-by-nilpotent group is isolated.The same is true for an ordered polycyclic group.Examples are given to show that maximal partial orders need not be isolated in torsionfree polycyclic groups, nor in ordered centre-by-metabelian groups.