2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226070We give a survey of some recent papers by the authors and Masaaki Wada relating the twisted Alexander polynomial with a partial order on the set of prime knots. We also give examples and pose open problems.This is the version published by Geometry & Topology Monographs on 25 February 2008Geometric TopologyAlgebraic Topology57M25, 57M05Twisted Alexander polynomials and a partial order on the set of prime knotstext