2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/180804We show that partial dynamical symmetries (PDS) can occur at critical-points of quantum phase transitions, in which case, underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several types of PDS are demonstrated with the example of critical-point Hamiltonians for first- and second-order transitions in the framework of the interacting boson model, whose dynamical symmetries correspond to different shape-phases in nuclei.4 pages, 5 figures, minor adjustments to PRL requirements. PRL in pressNuclear TheoryStatistical Mechanicstext