2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156096This paper investigates conditions under which a given automorphism of a residually torsion-free nilpotent group respects some ordering of the group. For free groups and surface groups, this has relevance to ordering the fundamental groups of three-dimensional manifolds which fibre over the circle.v2: 9 pages, minor changes, to appear in J. AlgebraGroup Theory20F60 (Primary) 06F15, 20F34, 57M25 (Secondary)text